{"id":2775,"date":"2018-12-11T13:46:25","date_gmt":"2018-12-11T18:46:25","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/chapter\/add-and-subtract-polynomials\/"},"modified":"2018-12-11T13:46:25","modified_gmt":"2018-12-11T18:46:25","slug":"add-and-subtract-polynomials","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/chapter\/add-and-subtract-polynomials\/","title":{"raw":"Add and Subtract Polynomials","rendered":"Add and Subtract Polynomials"},"content":{"raw":"\n[latexpage]<div class=\"textbox textbox--learning-objectives\"><h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>By the end of this section, you will be able to: <ul><li>Determine the degree of polynomials<\/li><li>Add and subtract polynomials<\/li><li>Evaluate a polynomial function for a given value<\/li><li>Add and subtract polynomial functions<\/li><\/ul><\/div><div data-type=\"note\" class=\"be-prepared\"><p>Before you get started, take this readiness quiz.<\/p><ol id=\"fs-id1167836415169\" type=\"1\"><li>Simplify: \\(3{x}^{2}+3x+1+8{x}^{2}+5x+5.\\)<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167836652573\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>Subtract: \\(\\left(5n+8\\right)-\\left(2n-1\\right).\\)<div data-type=\"newline\"><br><\/div>If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167829586631\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>Evaluate: \\(4x{y}^{2}\\) when \\(x=-2\\) and \\(y=5.\\)<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/05eab039-6d1c-4d80-8c8c-94469164a52c#fs-id1167832053133\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><\/ol><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836299901\"><h3 data-type=\"title\">Determine the Degree of Polynomials<\/h3><p id=\"fs-id1167836319331\">We have learned that a <em data-effect=\"italics\">term<\/em> is a constant or the product of a constant and one or more variables. A <span data-type=\"term\">monomial<\/span> is an algebraic expression with one term. When it is of the form \\(a{x}^{m},\\) where <em data-effect=\"italics\">a<\/em> is a constant and <em data-effect=\"italics\">m<\/em> is a whole number, it is called a monomial in one variable. Some examples of monomial in one variable are. Monomials can also have more than one variable such as and \\(-4{a}^{2}{b}^{3}{c}^{2}.\\)<\/p><div data-type=\"note\"><div data-type=\"title\">Monomial<\/div><p id=\"fs-id1167824734983\">A <strong data-effect=\"bold\">monomial<\/strong> is an algebraic expression with one term.<\/p><p id=\"fs-id1167836409519\">A monomial in one variable is a term of the form \\(a{x}^{m},\\) where <em data-effect=\"italics\">a<\/em> is a constant and <em data-effect=\"italics\">m<\/em> is a whole number.<\/p><\/div><p id=\"fs-id1167833023042\">A monomial, or two or more monomials combined by addition or subtraction, is a <span data-type=\"term\">polynomial<\/span>. Some polynomials have special names, based on the number of terms. A monomial is a polynomial with exactly one term. A binomial has exactly two terms, and a <span data-type=\"term\">trinomial<\/span> has exactly three terms. There are no special names for polynomials with more than three terms.<\/p><div data-type=\"note\" id=\"fs-id1167829688772\"><div data-type=\"title\">Polynomials<\/div><p id=\"fs-id1167836481441\"><strong data-effect=\"bold\">polynomial<\/strong>\u2014A monomial, or two or more algebraic terms combined by addition or subtraction is a polynomial.<\/p><p id=\"fs-id1167829628029\"><strong data-effect=\"bold\">monomial<\/strong>\u2014A polynomial with exactly one term is called a monomial.<\/p><p id=\"fs-id1167829720442\"><strong data-effect=\"bold\">binomial<\/strong>\u2014A polynomial with exactly two terms is called a binomial.<\/p><p id=\"fs-id1167836510464\"><strong data-effect=\"bold\">trinomial<\/strong>\u2014A polynomial with exactly three terms is called a trinomial.<\/p><\/div><p id=\"fs-id1167836349269\">Here are some examples of polynomials.<\/p><table id=\"fs-id1167829661616\" class=\"unnumbered\" summary=\"This table has five columns and four rows. The first row is for polynomials and lists three examples: y plus 1, 4 a squared minus 7 a b plus 2 b squared, 4 x to the fourth power plus x cubed plus 8 x squared minus 9 x plus 1. The second row is for monomials and lists four examples: 14, 8 y squared, minus 9 x cubed y to the fifth power, and negative 12 a cubed b squared c. The third row is for binomials and lists four examples: a plus 7 b, 4 x square minus y squared, y squared minus 16, and 3 p cubed q minus 9 p squared q. The fourth row is for trinomials and list four examples: x squared minus 7 x plus 12, 9 m squared plus 2 mn minus 8 n squared, 6 k to the fourth power minus k cubed plus 8 k, and z to the fourth power plus 3z squared minus 1.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Polynomial<\/td><td data-valign=\"top\" data-align=\"left\">\\(y+1\\)<\/td><td data-valign=\"top\" data-align=\"left\">\\(4{a}^{2}-7ab+2{b}^{2}\\)<\/td><td data-valign=\"top\" data-align=\"left\">\\(4{x}^{4}+{x}^{3}+8{x}^{2}-9x+1\\)<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Monomial<\/td><td data-valign=\"top\" data-align=\"left\">14<\/td><td data-valign=\"top\" data-align=\"left\">\\(8{y}^{2}\\)<\/td><td data-valign=\"top\" data-align=\"left\">\\(-9{x}^{3}{y}^{5}\\)<\/td><td data-valign=\"top\" data-align=\"left\">\\(-13{a}^{3}{b}^{2}c\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Binomial<\/td><td data-valign=\"top\" data-align=\"left\">\\(a+7b\\)<\/td><td data-valign=\"top\" data-align=\"left\">\\(4{x}^{2}-{y}^{2}\\)<\/td><td data-valign=\"top\" data-align=\"left\">\\({y}^{2}-16\\)<\/td><td data-valign=\"top\" data-align=\"left\">\\(3{p}^{3}q-9{p}^{2}q\\)<\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Trinomial<\/td><td data-valign=\"top\" data-align=\"left\">\\({x}^{2}-7x+12\\)<\/td><td data-valign=\"top\" data-align=\"left\">\\(9{m}^{2}+2mn-8{n}^{2}\\)<\/td><td data-valign=\"top\" data-align=\"left\">\\(6{k}^{4}-{k}^{3}+8k\\)<\/td><td data-valign=\"top\" data-align=\"left\">\\({z}^{4}+3{z}^{2}-1\\)<\/td><\/tr><\/tbody><\/table><p>Notice that every monomial, binomial, and trinomial is also a polynomial. They are just special members of the \u201cfamily\u201d of polynomials and so they have special names. We use the words <em data-effect=\"italics\">monomial<\/em>, <em data-effect=\"italics\">binomial<\/em>, and <em data-effect=\"italics\">trinomial<\/em> when referring to these special polynomials and just call all the rest <em data-effect=\"italics\">polynomials<\/em>.<\/p><p id=\"fs-id1167836298253\">The <span data-type=\"term\">degree of a polynomial<\/span> and the degree of its terms are determined by the exponents of the variable.<\/p><p id=\"fs-id1167836322222\">A monomial that has no variable, just a constant, is a special case. The <span data-type=\"term\">degree of a constant<\/span> is 0.<\/p><div data-type=\"note\" id=\"fs-id1167836310024\"><div data-type=\"title\">Degree of a Polynomial<\/div><p>The <strong data-effect=\"bold\">degree of a term<\/strong> is the sum of the exponents of its variables.<\/p><p>The <strong data-effect=\"bold\">degree of a constant<\/strong> is 0.<\/p><p>The <strong data-effect=\"bold\">degree of a polynomial<\/strong> is the highest degree of all its terms.<\/p><\/div><p>Let\u2019s see how this works by looking at several polynomials. We\u2019ll take it step by step, starting with monomials, and then progressing to polynomials with more terms.<\/p><p id=\"fs-id1167836628336\">Let's start by looking at a monomial. The monomial \\(8a{b}^{2}\\) has two variables <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em>. To find the degree we need to find the sum of the exponents. The variable a doesn't have an exponent written, but remember that means the exponent is 1. The exponent of <em data-effect=\"italics\">b<\/em> is 2. The sum of the exponents, \\(1+2,\\) is 3 so the degree is 3.<\/p><span data-type=\"media\" data-alt=\"The polynomial is 8 a b squared. The exponents of the variables are 1 and 2 so the degree of the monomial is 1 plus 2 which equals 3.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_001_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The polynomial is 8 a b squared. The exponents of the variables are 1 and 2 so the degree of the monomial is 1 plus 2 which equals 3.\"><\/span><p id=\"fs-id1167836508452\">Here are some additional examples.<\/p><span data-type=\"media\" id=\"fs-id1167836282723\" data-alt=\"Monomial examples: 14 has degree 0, 8 a b squared has degree 3, negative 9 x cubed y to the fifth power has degree 8, negative 13 a has degree 1. Binomial examples: The terms in h plus 7 have degree 1 and 0 so the degree of the whole polynomial is 1. The terms in 7 b squared minus 3 b have degree 2 and 1 so the degree of the whole polynomial is 2. The terms in z squared y squared minus 25 have degree 4 and 0 so the degree of the whole polynomial is 4. The terms in 4 n cubed minus 8 n squared have degree 3 and 2 so the degree of the whole polynomial is 3. Trinomial examples: The terms in x squared minus 12 x plus 27 have degree 2, 1 and 0 so the degree of the whole polynomial is 2. The terms in 9 a squared plus 6 a b plus b squared have degree 2, 2, and 2 so the degree of the whole polynomial is 2. The terms in 6 m to the fourth power minus m cubed n squared plus 8 m n to the fifth power have degree 4, 5, and 6 so the degree of the whole polynomial is 6. The terms in z to the fourth power plus 3 z squared minus 1 have degree 4, 2, and 0 so the degree of the whole polynomial is 4. Polynomial examples: The terms in y minus 1 have degree 1 and 0 so the degree of the whole polynomial is 1. The terms in 3 y squared minus 2 y minus 5 have degree 2, 1, 0 so the degree of the whole polynomial is 2. The terms in 4 x to the fourth power plus x cubed plus eight x squared minus 9 x plus 1 have degree 4, 3, 2, 1, and 0 so the degree of the whole polynomial is 4.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_002_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Monomial examples: 14 has degree 0, 8 a b squared has degree 3, negative 9 x cubed y to the fifth power has degree 8, negative 13 a has degree 1. Binomial examples: The terms in h plus 7 have degree 1 and 0 so the degree of the whole polynomial is 1. The terms in 7 b squared minus 3 b have degree 2 and 1 so the degree of the whole polynomial is 2. The terms in z squared y squared minus 25 have degree 4 and 0 so the degree of the whole polynomial is 4. The terms in 4 n cubed minus 8 n squared have degree 3 and 2 so the degree of the whole polynomial is 3. Trinomial examples: The terms in x squared minus 12 x plus 27 have degree 2, 1 and 0 so the degree of the whole polynomial is 2. The terms in 9 a squared plus 6 a b plus b squared have degree 2, 2, and 2 so the degree of the whole polynomial is 2. The terms in 6 m to the fourth power minus m cubed n squared plus 8 m n to the fifth power have degree 4, 5, and 6 so the degree of the whole polynomial is 6. The terms in z to the fourth power plus 3 z squared minus 1 have degree 4, 2, and 0 so the degree of the whole polynomial is 4. Polynomial examples: The terms in y minus 1 have degree 1 and 0 so the degree of the whole polynomial is 1. The terms in 3 y squared minus 2 y minus 5 have degree 2, 1, 0 so the degree of the whole polynomial is 2. The terms in 4 x to the fourth power plus x cubed plus eight x squared minus 9 x plus 1 have degree 4, 3, 2, 1, and 0 so the degree of the whole polynomial is 4.\"><\/span><p id=\"fs-id1167836523638\">Working with polynomials is easier when you list the terms in descending order of degrees. When a polynomial is written this way, it is said to be in <span data-type=\"term\">standard form of a polynomial<\/span>. Get in the habit of writing the term with the highest degree first.<\/p><div data-type=\"example\" id=\"fs-id1167836415722\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836529152\"><div data-type=\"problem\" id=\"fs-id1167829694957\"><p id=\"fs-id1167836546580\">Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial.<\/p><p id=\"fs-id1167836456244\"><span class=\"token\">\u24d0<\/span>\\(7{y}^{2}-5y+3\\)<span class=\"token\">\u24d1<\/span>\\(-2{a}^{4}{b}^{2}\\)<span class=\"token\">\u24d2<\/span>\\(3{x}^{5}-4{x}^{3}-6{x}^{2}+x-8\\)<span class=\"token\">\u24d3<\/span>\\(2y-8x{y}^{3}\\)<span class=\"token\">\u24d4<\/span> 15<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836635375\"><table id=\"fs-id1167836357312\" class=\"unnumbered\" summary=\"This table has five columns. The first is labeled polynomials, the second is number of terms, the third is type, the fourth is degree of terms, and the fifth is degree of polynomial. The first row shows 7 y squared minus 5y plus 3 has 3 terms, trinomial, the degree of terms are 2, 1, 0, and the degree of the polynomial is 2. The second row shows minus 2 a to the fourth b squared has 1 term, monomial, degree of terms and degree of polynomial are both 4. The third row shows 3 x to the fifth power minus 4 x cubed minus 6 x squared plus x minus 8 has 5 terms, is a polynomial, and the degree of terms are 5, 3, 2, 0, and 1, so the degree of the polynomial is 5. The fourth row shows 2y minus 8 x y cubed has 2 terms, is a binomial, has degree of terms 1 and 5, and the degree of the polynomial is 4. The fifth row shows 14 which has 1 term and is a monomial with degree of terms and degree of polynomial 0.\" data-label=\"\"><thead><tr valign=\"top\"><th data-valign=\"top\" data-align=\"left\"><\/th><th data-valign=\"top\" data-align=\"left\">Polynomial<\/th><th data-valign=\"top\" data-align=\"left\">Number of terms<\/th><th data-valign=\"top\" data-align=\"left\">Type<\/th><th data-valign=\"top\" data-align=\"left\">Degree of terms<\/th><th data-valign=\"top\" data-align=\"left\">Degree of polynomial<\/th><\/tr><\/thead><tbody><tr valign=\"top\"><td data-valign=\"middle\" data-align=\"left\"><span class=\"token\">\u24d0<\/span><\/td><td data-valign=\"middle\" data-align=\"left\">\\(7{y}^{2}-5y+3\\)<\/td><td data-valign=\"middle\" data-align=\"center\">3<\/td><td data-valign=\"middle\" data-align=\"left\">Trinomial<\/td><td data-valign=\"middle\" data-align=\"center\">2, 1, 0<\/td><td data-valign=\"middle\" data-align=\"center\">2<\/td><\/tr><tr valign=\"top\"><td data-valign=\"middle\" data-align=\"left\"><span class=\"token\">\u24d1<\/span><\/td><td data-valign=\"middle\" data-align=\"left\">\\(-2{a}^{4}{b}^{2}\\)<\/td><td data-valign=\"middle\" data-align=\"center\">1<\/td><td data-valign=\"middle\" data-align=\"left\">Monomial<\/td><td data-valign=\"middle\" data-align=\"center\">4, 2<\/td><td data-valign=\"middle\" data-align=\"center\">6<\/td><\/tr><tr valign=\"top\"><td data-valign=\"middle\" data-align=\"left\"><span class=\"token\">\u24d2<\/span><\/td><td data-valign=\"middle\" data-align=\"left\">\\(3{x}^{5}-4{x}^{3}-6{x}^{2}+x-8\\)<\/td><td data-valign=\"middle\" data-align=\"center\">5<\/td><td data-valign=\"middle\" data-align=\"left\">Polynomial<\/td><td data-valign=\"middle\" data-align=\"center\">5, 3, 2, 1, 0<\/td><td data-valign=\"middle\" data-align=\"center\">5<\/td><\/tr><tr valign=\"top\"><td data-valign=\"middle\" data-align=\"left\"><span class=\"token\">\u24d3<\/span><\/td><td data-valign=\"middle\" data-align=\"left\">\\(2y-8x{y}^{3}\\)<\/td><td data-valign=\"middle\" data-align=\"center\">2<\/td><td data-valign=\"middle\" data-align=\"left\">Binomial<\/td><td data-valign=\"middle\" data-align=\"center\">1, 4<\/td><td data-valign=\"middle\" data-align=\"center\">4<\/td><\/tr><tr valign=\"top\"><td data-valign=\"middle\" data-align=\"left\"><span class=\"token\">\u24d4<\/span><\/td><td data-valign=\"middle\" data-align=\"left\">15<\/td><td data-valign=\"middle\" data-align=\"center\">1<\/td><td data-valign=\"middle\" data-align=\"left\">Monomial<\/td><td data-valign=\"middle\" data-align=\"center\">0<\/td><td data-valign=\"middle\" data-align=\"center\">0<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836518702\"><div data-type=\"problem\"><p>Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial.<\/p><p id=\"fs-id1167836544732\"><span class=\"token\">\u24d0<\/span>\\(-5\\)<span class=\"token\">\u24d1<\/span>\\(8{y}^{3}-7{y}^{2}-y-3\\)<span class=\"token\">\u24d2<\/span>\\(-3{x}^{2}y-5xy+9x{y}^{3}\\)<span class=\"token\">\u24d3<\/span>\\(81{m}^{2}-4{n}^{2}\\)<span class=\"token\">\u24d4<\/span>\\(-3{x}^{6}{y}^{3}z\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167836625437\"><span class=\"token\">\u24d0<\/span> monomial, 0<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> polynomial, 3 <span class=\"token\">\u24d2<\/span> trinomial, 3<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span> binomial, 2 <span class=\"token\">\u24d4<\/span> monomial, 10<\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836624239\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829751398\"><div data-type=\"problem\"><p id=\"fs-id1167836552504\">Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial.<\/p><p id=\"fs-id1167836553862\"><span class=\"token\">\u24d0<\/span>\\(64{k}^{3}-8\\)<span class=\"token\">\u24d1<\/span>\\(9{m}^{3}+4{m}^{2}-2\\)<span class=\"token\">\u24d2<\/span>\\(\\frac{5}{6}\\)<span class=\"token\">\u24d3<\/span>\\(8{a}^{4}-7{a}^{3}b-6{a}^{2}{b}^{2}-4a{b}^{3}+7{b}^{4}\\)<span class=\"token\">\u24d4<\/span>\\(\\text{\u2212}{p}^{4}{q}^{3}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836574318\"><p id=\"fs-id1167829752758\"><span class=\"token\">\u24d0<\/span>binomial, 3 <span class=\"token\">\u24d1<\/span> trinomial, 3 <span class=\"token\">\u24d2<\/span> monomial, 0 <span class=\"token\">\u24d3<\/span> polynomial, 4 <span class=\"token\">\u24d4<\/span> monomial, 7<\/p><\/div><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\"><h3 data-type=\"title\">Add and Subtract Polynomials<\/h3><p id=\"fs-id1167836297171\">We have learned how to simplify expressions by combining like terms. Remember, like terms must have the same variables with the same exponent. Since monomials are terms, adding and subtracting monomials is the same as combining like terms. If the monomials are like terms, we just combine them by adding or subtracting the coefficients.<\/p><div data-type=\"example\" id=\"fs-id1167829908757\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167829589861\"><div data-type=\"problem\"><p id=\"fs-id1167836295565\">Add or subtract: <span class=\"token\">\u24d0<\/span> \\(25{y}^{2}+15{y}^{2}\\) <span class=\"token\">\u24d1<\/span> \\(16p{q}^{3}-\\left(-7p{q}^{3}\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836282025\"><p id=\"fs-id1167836341558\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{cccc}&amp; &amp; &amp; \\hfill \\phantom{\\rule{3em}{0ex}}25{y}^{2}+15{y}^{2}\\hfill \\\\ \\text{Combine like terms.}\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{3em}{0ex}}40{y}^{2}\\hfill \\end{array}\\)<p id=\"fs-id1167836362982\"><span class=\"token\">\u24d1<\/span><\/p><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{cccc}&amp; &amp; &amp; \\hfill \\phantom{\\rule{3em}{0ex}}16p{q}^{3}-\\left(-7p{q}^{3}\\right)\\hfill \\\\ \\text{Combine like terms.}\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{3em}{0ex}}23p{q}^{3}\\hfill \\end{array}\\)<\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836353044\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836390664\"><div data-type=\"problem\" id=\"fs-id1167829716743\"><p id=\"fs-id1167836392806\">Add or subtract: <span class=\"token\">\u24d0<\/span> \\(12{q}^{2}+9{q}^{2}\\) <span class=\"token\">\u24d1<\/span> \\(8m{n}^{3}-\\left(-5m{n}^{3}\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836389469\"><p id=\"fs-id1167833345172\"><span class=\"token\">\u24d0<\/span>\\(21{q}^{2}\\)<span class=\"token\">\u24d1<\/span>\\(13m{n}^{3}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836357323\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167833310117\"><div data-type=\"problem\" id=\"fs-id1167836693189\"><p id=\"fs-id1167836628342\">Add or subtract: <span class=\"token\">\u24d0<\/span> \\(-15{c}^{2}+8{c}^{2}\\) <span class=\"token\">\u24d1<\/span> \\(-15{y}^{2}{z}^{3}-\\left(-5{y}^{2}{z}^{3}\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836610409\"><p id=\"fs-id1167836613592\"><span class=\"token\">\u24d0<\/span>\\(-7{c}^{2}\\)<span class=\"token\">\u24d1<\/span>\\(-10{y}^{2}{z}^{3}\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167836299490\">Remember that like terms must have the same variables with the same exponents.<\/p><div data-type=\"example\" id=\"fs-id1167836700849\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836524855\"><div data-type=\"problem\" id=\"fs-id1167836615698\"><p>Simplify: <span class=\"token\">\u24d0<\/span> \\({a}^{2}+7{b}^{2}-6{a}^{2}\\) <span class=\"token\">\u24d1<\/span> \\({u}^{2}v+5{u}^{2}-3{v}^{2}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836692468\"><p id=\"fs-id1167836532785\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{cccc}&amp; &amp; &amp; \\hfill \\phantom{\\rule{9em}{0ex}}{a}^{2}+7{b}^{2}-6{a}^{2}\\hfill \\\\ \\text{Combine like terms.}\\hfill &amp; &amp; &amp; \\hfill \\phantom{\\rule{9em}{0ex}}-5{a}^{2}+7{b}^{2}\\hfill \\end{array}\\)<p><span class=\"token\">\u24d1<\/span><\/p><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{cccc}&amp; &amp; &amp; \\hfill {u}^{2}v+5{u}^{2}-3{v}^{2}\\hfill \\\\ \\begin{array}{c}\\text{There are no like terms to combine.}\\hfill \\\\ \\text{In this case, the polynomial is unchanged.}\\hfill \\end{array}\\hfill &amp; &amp; &amp; \\hfill {u}^{2}v+5{u}^{2}-3{v}^{2}\\hfill \\end{array}\\)<\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836571078\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836387371\"><div data-type=\"problem\" id=\"fs-id1167836560357\"><p id=\"fs-id1167836287957\">Add: <span class=\"token\">\u24d0<\/span> \\(8{y}^{2}+3{z}^{2}-3{y}^{2}\\) <span class=\"token\">\u24d1<\/span> \\({m}^{2}{n}^{2}-8{m}^{2}+4{n}^{2}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836528200\"><p id=\"fs-id1167836492113\"><span class=\"token\">\u24d0<\/span>\\(5{y}^{2}+3{z}^{2}\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\({m}^{2}{n}^{2}-8{m}^{2}+4{n}^{2}\\)<\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836756832\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167824584640\"><div data-type=\"problem\" id=\"fs-id1167824584769\"><p id=\"fs-id1167829597034\">Add: <span class=\"token\">\u24d0<\/span> \\(3{m}^{2}+{n}^{2}-7{m}^{2}\\) <span class=\"token\">\u24d1<\/span> \\(p{q}^{2}-6p-5{q}^{2}.\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167824737606\"><span class=\"token\">\u24d0<\/span>\\(-4{m}^{2}+{n}^{2}\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(p{q}^{2}-6p-5{q}^{2}\\)<\/div><\/div><\/div><p>We can think of adding and subtracting polynomials as just adding and subtracting a series of monomials. Look for the like terms\u2014those with the same variables and the same exponent. The Commutative Property allows us to rearrange the terms to put like terms together.<\/p><div data-type=\"example\" id=\"fs-id1167836289213\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167833139745\"><div data-type=\"problem\" id=\"fs-id1167833056480\"><p id=\"fs-id1167833056483\">Find the sum:\\(\\left(7{y}^{2}-2y+9\\right)+\\left(4{y}^{2}-8y-7\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829614243\"><p>\\(\\begin{array}{cccc}\\text{Identify like terms.}\\hfill &amp; &amp; &amp; \\hfill \\left(\\underset{____}{\\underset{____}{7{y}^{2}}}-\\underset{___}{2y}+9\\right)+\\left(\\underset{____}{\\underset{____}{4{y}^{2}}}-\\underset{___}{8y}-7\\right)\\hfill \\\\ \\begin{array}{c}\\text{Rewrite without the parentheses,}\\hfill \\\\ \\text{rearranging to get the like terms together.}\\hfill \\end{array}\\hfill &amp; &amp; &amp; \\hfill \\underset{_________}{\\underset{_________}{7{y}^{2}+4{y}^{2}}}-\\underset{_______}{2y-8y}+9-7\\hfill \\\\ \\text{Combine like terms.}\\hfill &amp; &amp; &amp; \\hfill 11{y}^{2}-10y+2\\hfill \\end{array}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836539576\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836447632\"><div data-type=\"problem\" id=\"fs-id1167836309244\"><p id=\"fs-id1167836309246\">Find the sum: \\(\\left(7{x}^{2}-4x+5\\right)+\\left({x}^{2}-7x+3\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829586793\"><p id=\"fs-id1167829586795\">\\(8{x}^{2}-11x+8\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167824736146\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167833385425\"><div data-type=\"problem\" id=\"fs-id1167833385427\"><p id=\"fs-id1167833071635\">Find the sum: \\(\\left(14{y}^{2}+6y-4\\right)+\\left(3{y}^{2}+8y+5\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167825703487\"><p id=\"fs-id1167825703489\">\\(17{y}^{2}+14y+1\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1171790896470\">Be careful with the signs as you distribute while subtracting the polynomials in the next example.<\/p><div data-type=\"example\" id=\"fs-id1167829749490\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167829749492\"><div data-type=\"problem\" id=\"fs-id1167836522315\"><p id=\"fs-id1167836522317\">Find the difference: \\(\\left(9{w}^{2}-7w+5\\right)-\\left(2{w}^{2}-4\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836731036\"><p id=\"fs-id1167836756613\">\\(\\begin{array}{cccc}&amp; &amp; &amp; \\hfill \\left(9{w}^{2}-7w+5\\right)-\\left(2{w}^{2}-4\\right)\\hfill \\\\ \\text{Distribute and identify like terms.}\\hfill &amp; &amp; &amp; \\hfill \\underset{____}{\\underset{____}{9{w}^{2}}}-\\underset{___}{7w}+5-\\underset{____}{\\underset{____}{2{w}^{2}}}+4\\hfill \\\\ \\text{Rearrange the terms.}\\hfill &amp; &amp; &amp; \\hfill \\underset{__________}{\\underset{__________}{9{w}^{2}-2{w}^{2}}}-\\underset{___}{7w}+5+4\\hfill \\\\ \\text{Combine like terms.}\\hfill &amp; &amp; &amp; \\hfill 7{w}^{2}-7w+9\\hfill \\end{array}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833339032\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167833339035\"><div data-type=\"problem\" id=\"fs-id1167836620467\"><p id=\"fs-id1167836620470\">Find the difference: \\(\\left(8{x}^{2}+3x-19\\right)-\\left(7{x}^{2}-14\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836543282\"><p id=\"fs-id1167836543285\">\\({x}^{2}+3x-5\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829585676\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829585679\"><div data-type=\"problem\" id=\"fs-id1167836447528\"><p id=\"fs-id1167836447530\">Find the difference: \\(\\left(9{b}^{2}-5b-4\\right)-\\left(3{b}^{2}-5b-7\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829832094\"><p id=\"fs-id1167836533016\">\\(6{b}^{2}+3\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1171790290366\">To subtract \\(a\\) from \\(b,\\) we write it as \\(b-a,\\) placing the \\(b\\) first.<\/p><div data-type=\"example\" id=\"fs-id1167833049950\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167833049952\"><div data-type=\"problem\"><p id=\"fs-id1167833339601\">Subtract \\(\\left({p}^{2}+10pq-2{q}^{2}\\right)\\) from \\(\\left({p}^{2}+{q}^{2}\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836706818\"><p id=\"fs-id1167833057701\">\\(\\begin{array}{cccc}&amp; &amp; &amp; \\hfill \\left({p}^{2}+{q}^{2}\\right)-\\left({p}^{2}+10pq-2{q}^{2}\\right)\\hfill \\\\ \\text{Distribute.}\\hfill &amp; &amp; &amp; \\hfill {p}^{2}+{q}^{2}-{p}^{2}-10pq+2{q}^{2}\\hfill \\\\ \\text{Rearrange the terms, to put like terms together.}\\hfill &amp; &amp; &amp; \\hfill {p}^{2}-{p}^{2}-10pq+{q}^{2}+2{q}^{2}\\hfill \\\\ \\text{Combine like terms.}\\hfill &amp; &amp; &amp; \\hfill -10p{q}^{2}+3{q}^{2}\\hfill \\end{array}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167824733970\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836416627\"><div data-type=\"problem\" id=\"fs-id1167836416629\"><p id=\"fs-id1167836416631\">Subtract \\(\\left({a}^{2}+5ab-6{b}^{2}\\right)\\) from \\(\\left({a}^{2}+{b}^{2}\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836557087\"><p id=\"fs-id1167836557089\">\\(-5ab+7{b}^{2}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829853708\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829853711\"><div data-type=\"problem\" id=\"fs-id1167836493326\"><p id=\"fs-id1167836493328\">Subtract \\(\\left({m}^{2}-7mn-3{n}^{2}\\right)\\) from \\(\\left({m}^{2}+{n}^{2}\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836665216\"><p id=\"fs-id1167836665218\">\\(7mn+4{n}^{2}\\)<\/p><\/div><\/div><\/div><div data-type=\"example\" class=\"textbox textbox--examples\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167833412566\"><p id=\"fs-id1167836730201\">Find the sum: \\(\\left({u}^{2}-6uv+5{v}^{2}\\right)+\\left(3{u}^{2}+2uv\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836558032\"><p id=\"fs-id1167836558034\">\\(\\begin{array}{cccc}&amp; &amp; &amp; \\hfill \\left({u}^{2}-6uv+5{v}^{2}\\right)+\\left(3{u}^{2}+2uv\\right)\\hfill \\\\ \\\\ \\\\ \\text{Distribute.}\\hfill &amp; &amp; &amp; \\hfill {u}^{2}-6uv+5{v}^{2}+3{u}^{2}+2uv\\hfill \\\\ \\\\ \\\\ \\text{Rearrange the terms to put like terms together.}\\hfill &amp; &amp; &amp; \\hfill {u}^{2}+3{u}^{2}-6uv+2uv+5{v}^{2}\\hfill \\\\ \\\\ \\\\ \\text{Combine like terms.}\\hfill &amp; &amp; &amp; \\hfill 4{u}^{2}-4uv+5{v}^{2}\\hfill \\end{array}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836552919\"><div data-type=\"problem\" id=\"fs-id1167836552921\"><p id=\"fs-id1167833382187\">Find the sum: \\(\\left(3{x}^{2}-4xy+5{y}^{2}\\right)+\\left(2{x}^{2}-xy\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836424170\"><p id=\"fs-id1167836602764\">\\(5{x}^{2}-5xy+5{y}^{2}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836689192\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836689195\"><div data-type=\"problem\" id=\"fs-id1167836689197\"><p id=\"fs-id1167836624073\">Find the sum: \\(\\left(2{x}^{2}-3xy-2{y}^{2}\\right)+\\left(5{x}^{2}-3xy\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833036790\"><p id=\"fs-id1167836756749\">\\(7{x}^{2}-6xy-2{y}^{2}\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1171792799230\">When we add and subtract more than two polynomials, the process is the same.<\/p><div data-type=\"example\" id=\"fs-id1167836423838\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836423840\"><div data-type=\"problem\" id=\"fs-id1167836507496\"><p id=\"fs-id1167836507498\">Simplify: \\(\\left({a}^{3}-{a}^{2}b\\right)-\\left(a{b}^{2}+{b}^{3}\\right)+\\left({a}^{2}b+a{b}^{2}\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836560662\"><p id=\"fs-id1167836560664\">\\(\\begin{array}{cccc}&amp; &amp; &amp; \\hfill \\left({a}^{3}-{a}^{2}b\\right)-\\left(a{b}^{2}+{b}^{3}\\right)+\\left({a}^{2}b+a{b}^{2}\\right)\\hfill \\\\ \\\\ \\\\ \\text{Distribute.}\\hfill &amp; &amp; &amp; \\hfill {a}^{3}-{a}^{2}b-a{b}^{2}-{b}^{3}+{a}^{2}b+a{b}^{2}\\hfill \\\\ \\\\ \\\\ \\text{Rewrite without the parentheses,}\\hfill &amp; &amp; &amp; \\\\ \\text{rearranging to get the like terms together.}\\hfill &amp; &amp; &amp; \\hfill {a}^{3}-{a}^{2}b+{a}^{2}b-a{b}^{2}+a{b}^{2}-{b}^{3}\\hfill \\\\ \\\\ \\\\ \\text{Combine like terms.}\\hfill &amp; &amp; &amp; \\hfill {a}^{3}-{b}^{3}\\hfill \\end{array}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167829594555\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167829594558\"><div data-type=\"problem\" id=\"fs-id1167836493517\"><p id=\"fs-id1167836493519\">Simplify: \\(\\left({x}^{3}-{x}^{2}y\\right)-\\left(x{y}^{2}+{y}^{3}\\right)+\\left({x}^{2}y+x{y}^{2}\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832961272\"><p id=\"fs-id1167832961274\">\\({x}^{3}+{y}^{3}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836293746\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836293749\"><div data-type=\"problem\" id=\"fs-id1167836293752\"><p id=\"fs-id1167829930564\">Simplify: \\(\\left({p}^{3}-{p}^{2}q\\right)+\\left(p{q}^{2}+{q}^{3}\\right)-\\left({p}^{2}q+p{q}^{2}\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833030913\"><p id=\"fs-id1167833030915\">\\({p}^{3}-3{p}^{2}q+{q}^{3}\\)<\/p><\/div><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836624599\"><h3 data-type=\"title\">Evaluate a Polynomial Function for a Given Value<\/h3><p id=\"fs-id1167833381572\">A <span data-type=\"term\">polynomial function<\/span> is a function defined by a polynomial. For example, \\(f\\left(x\\right)={x}^{2}+5x+6\\) and \\(g\\left(x\\right)=3x-4\\) are polynomial functions, because \\({x}^{2}+5x+6\\) and \\(3x-4\\) are polynomials.<\/p><div data-type=\"note\" id=\"fs-id1167836511381\"><div data-type=\"title\">Polynomial Function<\/div><p id=\"fs-id1167836596338\">A <strong data-effect=\"bold\">polynomial function<\/strong> is a function whose range values are defined by a polynomial.<\/p><\/div><p id=\"fs-id1167836294033\">In <a href=\"\/contents\/4d690921-1182-4ad3-86e0-7f849efbd233\" class=\"target-chapter\">Graphs and Functions<\/a>, where we first introduced functions, we learned that evaluating a function means to find the value of \\(f\\left(x\\right)\\) for a given value of <em data-effect=\"italics\">x<\/em>. To evaluate a polynomial function, we will substitute the given value for the variable and then simplify using the order of operations.<\/p><div data-type=\"example\" id=\"fs-id1167836619473\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836619475\"><div data-type=\"problem\" id=\"fs-id1167829694499\"><p id=\"fs-id1167829694501\">For the function \\(f\\left(x\\right)=5{x}^{2}-8x+4\\) find: <span class=\"token\">\u24d0<\/span> \\(f\\left(4\\right)\\) <span class=\"token\">\u24d1<\/span> \\(f\\left(-2\\right)\\) <span class=\"token\">\u24d2<\/span> \\(f\\left(0\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836477533\"><p id=\"fs-id1167836477535\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><table id=\"fs-id1167829741803\" class=\"unnumbered unstyled\" summary=\"The image shows a series of equations with instructions. The first equation is the function equation f of x equals 5 x squared minus 8 x plus 4. To find f of 4, substitute 4 for x. The second equation is f of 4 equals 5 times 4 squared minus 8 times 4 plus 4. The 4\u2019s replacing x are emphasized. The remaining equations show how to simplify the right side of the equation using the order of operations. The third equation is f of 4 equals 5 times 16 minus 8 times 4 plus 4. The fourth equation is f of 4 equals 80 minus 32 plus 4. The last equation is f of 4 equals 52.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836391910\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_004b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_004a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span>\u2003\u2003<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829597649\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_004c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify the exponents.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833061150\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_004d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Multiply.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836635636\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_004e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833056901\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_004f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><p id=\"fs-id1167836557376\"><span class=\"token\">\u24d1<\/span><\/p><div data-type=\"newline\"><br><\/div><table id=\"fs-id1167836557383\" class=\"unnumbered unstyled\" summary=\"The image shows a series of equations with instructions. The first equation is the function equation f of x equals 5 x squared minus 8 x plus 4. To find f of negative 2, substitute negative 2 for x. The second equation is f of negative 2 equals 5 times negative 2 squared minus 8 times negative 2 plus 4. The negative 2\u2019s replacing x are emphasized. The remaining equations show how to simplify the right side of the equation using the order of operations. The third equation is f of negative 2 equals 5 times 4 minus 8 times negative 2 plus 4. The fourth equation is f of negative 2 equals 20 plus 16 plus 4. The last equation is f of negative 2 equals 40.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836520680\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_005b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836515645\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_005a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span>\u2003<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167832999661\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_005c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify the exponents.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836362540\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_005d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Multiply.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836738242\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_005e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836534829\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_005f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><p id=\"fs-id1167836700907\"><span class=\"token\">\u24d2<\/span><\/p><div data-type=\"newline\"><br><\/div><table id=\"fs-id1167836606920\" class=\"unnumbered unstyled\" summary=\"The image shows a series of equations with instructions. The first equation is the function equation f of x equals 5 x squared minus 8 x plus 4. To find f of 0, substitute 0 for x. The second equation is f of 0 equals 5 times 0 squared minus 8 times 0 plus 4. The 0\u2019s replacing x are emphasized. The remaining equations show how to simplify the right side of the equation using the order of operations. The third equation is f of 0 equals 5 times 0 minus 8 times 0 plus 4. The fourth equation is f of 0 equals 0 plus 0 plus 4. The last equation is f of 0 equals 4.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829690356\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_006b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833059281a\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_006a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span>\u2003\u2003<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833059281\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_006c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify the exponents.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836492694\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_006d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Multiply.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833339022\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_006e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Simplify.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167832999463\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_006f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836532480\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836532484\"><div data-type=\"problem\" id=\"fs-id1167836532486\"><p id=\"fs-id1167836520974\">For the function \\(f\\left(x\\right)=3{x}^{2}+2x-15,\\) find <span class=\"token\">\u24d0<\/span> \\(f\\left(3\\right)\\) <span class=\"token\">\u24d1<\/span> \\(f\\left(-5\\right)\\) <span class=\"token\">\u24d2<\/span> \\(f\\left(0\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836560811\"><p id=\"fs-id1167836560813\"><span class=\"token\">\u24d0<\/span> 18 <span class=\"token\">\u24d1<\/span> 50 <span class=\"token\">\u24d2<\/span> \\(-15\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836377469\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836377474\"><div data-type=\"problem\" id=\"fs-id1167836377476\"><p id=\"fs-id1167836515904\">For the function \\(g\\left(x\\right)=5{x}^{2}-x-4,\\) find <span class=\"token\">\u24d0<\/span> \\(g\\left(-2\\right)\\) <span class=\"token\">\u24d1<\/span> \\(g\\left(-1\\right)\\) <span class=\"token\">\u24d2<\/span> \\(g\\left(0\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836507429\"><p id=\"fs-id1167836507431\"><span class=\"token\">\u24d0<\/span> 20 <span class=\"token\">\u24d1<\/span> 2 <span class=\"token\">\u24d2<\/span> \\(-4\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167829580335\">The polynomial functions similar to the one in the next example are used in many fields to determine the height of an object at some time after it is projected into the air. The polynomial in the next function is used specifically for dropping something from 250 ft.<\/p><div data-type=\"example\" id=\"fs-id1167836494121\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836494123\"><div data-type=\"problem\" id=\"fs-id1167836494125\"><p id=\"fs-id1167836494127\">The polynomial function \\(h\\left(t\\right)=-16{t}^{2}+250\\) gives the height of a ball <em data-effect=\"italics\">t<\/em> seconds after it is dropped from a 250-foot tall building. Find the height after \\(t=2\\) seconds.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836596028\"><p id=\"fs-id1167836596030\">\\(\\begin{array}{cccc}&amp; &amp; &amp; h\\left(t\\right)=-16{t}^{2}+250\\hfill \\\\ \\\\ \\text{To find}\\phantom{\\rule{0.2em}{0ex}}h\\left(2\\right),\\phantom{\\rule{0.2em}{0ex}}\\text{substitute}\\phantom{\\rule{0.2em}{0ex}}t=2.\\hfill &amp; &amp; &amp; h\\left(2\\right)=-16{\\left(2\\right)}^{2}+250\\hfill \\\\ \\text{Simplify.}\\hfill &amp; &amp; &amp; h\\left(2\\right)=-16\u00b74+250\\hfill \\\\ \\\\ \\text{Simplify.}\\hfill &amp; &amp; &amp; h\\left(2\\right)=-64+250\\hfill \\\\ \\\\ \\text{Simplify.}\\hfill &amp; &amp; &amp; h\\left(2\\right)=186\\hfill \\\\ &amp; &amp; &amp; \\text{After 2 seconds the height of the ball is 186 feet.}\\hfill \\end{array}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836628296\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167836606842\"><div data-type=\"problem\"><p id=\"fs-id1167836606847\">The polynomial function \\(h\\left(t\\right)=-16{t}^{2}+150\\) gives the height of a stone <em data-effect=\"italics\">t<\/em> seconds after it is dropped from a 150-foot tall cliff. Find the height after \\(t=0\\) seconds (the initial height of the object).<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836730595\"><p id=\"fs-id1167836706618\">The height is \\(150\\) feet.<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167833082429\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167833082432\"><div data-type=\"problem\" id=\"fs-id1167836546926\"><p id=\"fs-id1167836546928\">The polynomial function \\(h\\left(t\\right)=-16{t}^{2}+175\\) gives the height of a ball <em data-effect=\"italics\">t<\/em> seconds after it is dropped from a 175-foot tall bridge. Find the height after \\(t=3\\) seconds.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833051269\"><p id=\"fs-id1167833051271\">The height is 31 feet.<\/p><\/div><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167829719032\"><h3 data-type=\"title\">Add and Subtract Polynomial Functions<\/h3><p id=\"fs-id1167833224796\">Just as polynomials can be added and subtracted, polynomial functions can also be added and subtracted.<\/p><div data-type=\"note\" id=\"fs-id1167833224799\"><div data-type=\"title\">Addition and Subtraction of Polynomial Functions<\/div><p id=\"fs-id1167833224804\">For functions \\(f\\left(x\\right)\\) and \\(g\\left(x\\right),\\)<\/p><div data-type=\"equation\" id=\"fs-id1167836508945\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{c}\\left(f+g\\right)\\left(x\\right)=f\\left(x\\right)+g\\left(x\\right)\\hfill \\\\ \\left(f-g\\right)\\left(x\\right)=f\\left(x\\right)-g\\left(x\\right)\\hfill \\end{array}\\)<\/div><\/div><div data-type=\"example\" id=\"fs-id1167836717235\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167836717237\"><div data-type=\"problem\" id=\"fs-id1167836717240\"><p id=\"fs-id1167836717242\">For functions \\(f\\left(x\\right)=3{x}^{2}-5x+7\\) and \\(g\\left(x\\right)={x}^{2}-4x-3,\\) find:<\/p><p id=\"fs-id1167829872138\"><span class=\"token\">\u24d0<\/span>\\(\\left(f+g\\right)\\left(x\\right)\\)<span class=\"token\">\u24d1<\/span>\\(\\left(f+g\\right)\\left(3\\right)\\)<span class=\"token\">\u24d2<\/span>\\(\\left(f-g\\right)\\left(x\\right)\\)<span class=\"token\">\u24d3<\/span>\\(\\left(f-g\\right)\\left(-2\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832982204\"><p id=\"fs-id1167832982206\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div><table id=\"fs-id1167836391919\" class=\"unnumbered unstyled\" summary=\"The figure shows a series of equations in function notation. The first equation is the formula f plus g of x equals f of x plus g of x. Substituting f of x equals 3 x squared minus 5 x plus 7 and g of x equals x squared minus 4 x minus 3 into the formula results in the equation f plus g of x equals the quantity 3 x squared minus 5 x plus 7 in parentheses plus the quantity x squared minus 4 x minus 3 in parentheses. Rewriting without parentheses is the equation f plus g of x equals 3 x squared minus 5 x plus 7 plus x squared minus 4 x minus 3. Putting like terms together results in the equation f plus g of x equals 3 x squared plus x squared minus 5 x minus 4 x plus 7 minus 3. Combining like terms results in the fully simplified function equation f plus g of x equals 4 x squared minus 9 x plus 4.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836326099\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_007b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829861746\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_007a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836624089\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_007c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Rewrite without the parentheses.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829695341\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_007d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Put like terms together.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829627739\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_007e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Combine like terms.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833407424\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_007f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><p id=\"fs-id1167836730613\"><span class=\"token\">\u24d1<\/span> In part (a) we found \\(\\left(f+g\\right)\\left(x\\right)\\) and now are asked to find \\(\\left(f+g\\right)\\left(3\\right).\\)<\/p><div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div> \\(\\begin{array}{cccc}&amp; &amp; &amp; \\left(f+g\\right)\\left(x\\right)=4{x}^{2}-9x+4\\hfill \\\\ \\\\ \\\\ \\text{To find}\\phantom{\\rule{0.2em}{0ex}}\\left(f+g\\right)\\left(3\\right),\\phantom{\\rule{0.2em}{0ex}}\\text{substitute}\\phantom{\\rule{0.2em}{0ex}}x=3.\\hfill &amp; &amp; &amp; \\left(f+g\\right)\\left(3\\right)=4{\\left(3\\right)}^{2}-9\u00b73+4\\hfill \\\\ \\\\ \\\\ &amp; &amp; &amp; \\left(f+g\\right)\\left(3\\right)=4\u00b79-9\u00b73+4\\hfill \\\\ \\\\ \\\\ &amp; &amp; &amp; \\left(f+g\\right)\\left(3\\right)=36-27+4\\hfill \\end{array}\\)<p id=\"fs-id1167836660081\">Notice that we could have found \\(\\left(f+g\\right)\\left(3\\right)\\) by first finding the values of \\(f\\left(3\\right)\\) and \\(g\\left(3\\right)\\) separately and then adding the results.<\/p><table id=\"fs-id1167829748066\" class=\"unnumbered unstyled\" summary=\"The figure shows a series of calculations to verify the last result. The first calculation is labeled Find f of 3. The first equation is the function equation f of x equals 3 x squared minus 5 x plus 7. The second equation is f of 3 equals 3 times 3 squared minus 5 times 3 plus 7, where the 3\u2019s are all emphasized. The third equation is f of 3 equals 19. The second calculation is labeled Find g of 3. The first equation is the function equation g of x equals x squared minus 4 x minus 3. The second equation is g of 3 equals 3 squared minus 4 times 3 minus 3. The 3\u2019s that replaced the x\u2019s are emphasized. The next equation is g of 3 equals negative 6. The last calculation is labeled Find f plus g of 3. The first equation is the formula f plus g of x equals f of x plus g of x. The second equation is f plus g of 3 equals f of 3 plus g of 3. Substituting f of 3 equals 19 and g of 3 equals negative 6 we get the equation f plus g of 3 equals 19 minus 6. The last equation is f plus g of 3 equals 13.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Find \\(f\\left(3\\right).\\)<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829743187\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829745681\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836614824\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Find \\(g\\left(3\\right).\\)<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833338871\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833024470\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167832945745\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008g_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Find \\(\\left(f+g\\right)\\left(3\\right).\\)<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829579194\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008h_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833066755\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008i_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836391940\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span>\\(\\phantom{\\rule{1.2em}{0ex}}\\)<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836536972\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008j_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836601705\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008k_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><p id=\"fs-id1167833378545\"><span class=\"token\">\u24d2<\/span><\/p><div data-type=\"newline\"><br><\/div><table id=\"fs-id1167832982035\" class=\"unnumbered unstyled\" summary=\"The figure shows a series of equations in function notation. The first equation is the formula f minus g of x equals f of x minus g of x. Substituting f of x equals 3 x squared minus 5 x plus 7 and g of x equals x squared minus 4 x minus 3 into the formula results in the equation f minus g of x equals the quantity 3 x squared minus 5 x plus 7 in parentheses minus the quantity x squared minus 4 x minus 3 in parentheses. Rewriting without parentheses is the equation f minus g of x equals 3 x squared minus 5 x plus 7 minus x squared plus 4 x plus 3. Putting like terms together results in the equation f minus g of x equals 3 x squared minus x squared minus 5 x plus 4 x plus 7 plus 3. Combining like terms results in the fully simplified function equation f minus g of x equals 2 x squared minus x plus 10.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836625927\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_009b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829593569\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_009a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829717196\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_009c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Rewrite without the parentheses.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833338979\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_009d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Put like terms together.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829692985\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_009e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Combine like terms.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833227243\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_009f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><p id=\"fs-id1167833060375\"><span class=\"token\">\u24d3<\/span><\/p><div data-type=\"newline\"><br><\/div><table id=\"fs-id1167832937173\" class=\"unnumbered unstyled\" summary=\"The figure shows a series of equations in function notation. The first equation is the equation f minus g of x equals 2 x squared minus x plus 10. To find f minus g of negative 2 substitute x equals negative 2. The second equation is f minus g of negative 2 equals 2 times negative 2 squared minus negative 2 plus 10. The next equation is f minus g of negative 2 equals 2 times 4 minus negative 2 plus 10. The next equation is f minus g of negative 2 equals 20.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829739277\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_010_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167824734625\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167824734629\"><div data-type=\"problem\" id=\"fs-id1167824734631\"><p id=\"fs-id1167824734633\">For functions \\(f\\left(x\\right)=2{x}^{2}-4x+3\\) and \\(g\\left(x\\right)={x}^{2}-2x-6,\\) find: <span class=\"token\">\u24d0<\/span> \\(\\left(f+g\\right)\\left(x\\right)\\) <span class=\"token\">\u24d1<\/span> \\(\\left(f+g\\right)\\left(3\\right)\\) <span class=\"token\">\u24d2<\/span> \\(\\left(f-g\\right)\\left(x\\right)\\) <span class=\"token\">\u24d3<\/span> \\(\\left(f-g\\right)\\left(-2\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829811159\"><p id=\"fs-id1167829811161\"><span class=\"token\">\u24d0<\/span>\\(\\left(f+g\\right)\\left(x\\right)=3{x}^{2}-6x-3\\)<span class=\"token\">\u24d1<\/span>\\(\\left(f+g\\right)\\left(3\\right)=6\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(f-g\\right)\\left(x\\right)={x}^{2}-2x+9\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span>\\(\\left(f-g\\right)\\left(-2\\right)=17\\)<\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836619815\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167830076287\"><div data-type=\"problem\" id=\"fs-id1167830076289\"><p id=\"fs-id1167830076291\">For functions \\(f\\left(x\\right)=5{x}^{2}-4x-1\\) and \\(g\\left(x\\right)={x}^{2}+3x+8,\\) find <span class=\"token\">\u24d0<\/span> \\(\\left(f+g\\right)\\left(x\\right)\\) <span class=\"token\">\u24d1<\/span> \\(\\left(f+g\\right)\\left(3\\right)\\) <span class=\"token\">\u24d2<\/span> \\(\\left(f-g\\right)\\left(x\\right)\\) <span class=\"token\">\u24d3<\/span> \\(\\left(f-g\\right)\\left(-2\\right).\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167829614420\"><span class=\"token\">\u24d0<\/span>\\(\\left(f+g\\right)\\left(x\\right)=6{x}^{2}-x+7\\)<span class=\"token\">\u24d1<\/span>\\(\\left(f+g\\right)\\left(3\\right)=58\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(f-g\\right)\\left(x\\right)=4{x}^{2}-7x-9\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span>\\(\\left(f-g\\right)\\left(-2\\right)=21\\)<\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167836594852\" class=\"media-2\"><p id=\"fs-id1167836594856\">Access this online resource for additional instruction and practice with adding and subtracting polynomials.<\/p><ul id=\"fs-id1167836594861\" data-bullet-style=\"bullet\"><li><a href=\"https:\/\/openstax.org\/l\/37AddSubtrPoly\">Adding and Subtracting Polynomials<\/a><\/li><\/ul><\/div><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167824584895\"><h3 data-type=\"title\">Key Concepts<\/h3><ul id=\"fs-id1167829828750\" data-bullet-style=\"bullet\"><li><strong data-effect=\"bold\">Monomial<\/strong><ul id=\"fs-id1167836409466\" data-bullet-style=\"bullet\"><li>A <strong data-effect=\"bold\">monomial<\/strong> is an algebraic expression with one term.<\/li><li>A monomial in one variable is a term of the form \\(a{x}^{m},\\) where <em data-effect=\"italics\">a<\/em> is a constant and <em data-effect=\"italics\">m<\/em> is a whole number.<\/li><\/ul><\/li><li><strong data-effect=\"bold\">Polynomials<\/strong><ul id=\"fs-id1167836625101\" data-bullet-style=\"bullet\"><li><strong data-effect=\"bold\">Polynomial<\/strong>\u2014A monomial, or two or more algebraic terms combined by addition or subtraction is a polynomial.<\/li><li><strong data-effect=\"bold\">monomial<\/strong> \u2014A polynomial with exactly one term is called a monomial.<\/li><li><strong data-effect=\"bold\">binomial<\/strong> \u2014 A polynomial with exactly two terms is called a binomial.<\/li><li><strong data-effect=\"bold\">trinomial<\/strong> \u2014A polynomial with exactly three terms is called a trinomial.<\/li><\/ul><\/li><li><strong data-effect=\"bold\">Degree of a Polynomial<\/strong><ul id=\"fs-id1167836756827\" data-bullet-style=\"bullet\"><li>The <strong data-effect=\"bold\">degree of a term<\/strong> is the sum of the exponents of its variables.<\/li><li>The <strong data-effect=\"bold\">degree of a constant<\/strong> is 0.<\/li><li>The <strong data-effect=\"bold\">degree of a polynomial<\/strong> is the highest degree of all its terms.<\/li><\/ul><\/li><\/ul><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167829713312\"><div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1167829713317\"><h4 data-type=\"title\">Practice Makes Perfect<\/h4><p id=\"fs-id1167829713324\"><strong data-effect=\"bold\">Determine the Type of Polynomials<\/strong><\/p><p id=\"fs-id1167836408265\">In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial.<\/p><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167836408272\"><p id=\"fs-id1167836408274\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(47{x}^{5}-17{x}^{2}{y}^{3}+{y}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(5{c}^{3}+11{c}^{2}-c-8\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\frac{5}{9}ab+\\frac{1}{3}b\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span> 4<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span> \\(4pq+17\\)<\/div><div data-type=\"solution\" id=\"fs-id1167829627905\"><p id=\"fs-id1167829627907\"><span class=\"token\">\u24d0<\/span> trinomial, 5 <span class=\"token\">\u24d1<\/span> polynomial, 3 <span class=\"token\">\u24d2<\/span> binomial, 1 <span class=\"token\">\u24d3<\/span> monomial, 1<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span> binomial, 1<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836512992\"><div data-type=\"problem\" id=\"fs-id1167836512994\"><p id=\"fs-id1167836512996\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\({x}^{2}-{y}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(-13{c}^{4}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\({a}^{2}+2ab-7{b}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span>\\(4{x}^{2}{y}^{2}-3xy+8\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span> 19<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832937207\"><div data-type=\"problem\" id=\"fs-id1167832937209\"><p id=\"fs-id1167832937211\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(8y-5x\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\({y}^{2}-5yz-6{z}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\({y}^{3}-8{y}^{2}+2y-16\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span>\\(81a{b}^{4}-24{a}^{2}{b}^{2}+3b\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span>\\(-18\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836596290\"><p id=\"fs-id1167836596292\"><span class=\"token\">\u24d0<\/span> binomial <span class=\"token\">\u24d1<\/span> trinomial<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span> polynomial <span class=\"token\">\u24d3<\/span> trinomial<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span> monomial <\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833009337\"><div data-type=\"problem\" id=\"fs-id1167833009340\"><p id=\"fs-id1167833009342\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(11{y}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(-73\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(6{x}^{2}-3xy+4x-2y+{y}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span>\\(4{y}^{2}+17{z}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span>\\(5{c}^{3}+11{c}^{2}-c-8\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836321250\"><div data-type=\"problem\" id=\"fs-id1167836321253\"><p id=\"fs-id1167836321255\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(5{a}^{2}+12ab-7{b}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(18x{y}^{2}z\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(5x+2\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span>\\({y}^{3}-8{y}^{2}+2y-16\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span>\\(-24\\)<\/div><div data-type=\"solution\" id=\"fs-id1167829684015\"><p id=\"fs-id1167829684017\"><span class=\"token\">\u24d0<\/span>\\({2}^{0}\\)<span class=\"token\">\u24d1<\/span>\\({3}^{0}\\)<span class=\"token\">\u24d2<\/span>\\({1}^{0}\\)<span class=\"token\">\u24d3<\/span>\\({3}^{0}\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span>\\({0}^{0}\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829741538\"><div data-type=\"problem\" id=\"fs-id1167829741540\"><p id=\"fs-id1167829741542\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(9{y}^{3}-10{y}^{2}+2y-6\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(-12{p}^{3}q\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\({a}^{2}+9ab+18{b}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span>\\(20{x}^{2}{y}^{2}-10{a}^{2}{b}^{2}+30\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span> 17<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826131747\"><div data-type=\"problem\" id=\"fs-id1167826131749\"><p id=\"fs-id1167826131751\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(14s-29t\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\({z}^{2}-5z-6\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\({y}^{3}-8{y}^{2}z+2y{z}^{2}-16{z}^{3}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span>\\(23a{b}^{2}-14\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span>\\(-3\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836730500\"><p id=\"fs-id1167836730502\"><span class=\"token\">\u24d0<\/span>\\({1}^{0}\\)<span class=\"token\">\u24d1<\/span>\\({2}^{0}\\)<span class=\"token\">\u24d2<\/span>\\({3}^{0}\\)<span class=\"token\">\u24d3<\/span>\\({3}^{0}\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span>\\({0}^{0}\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836598350\"><div data-type=\"problem\" id=\"fs-id1167836598352\"><p id=\"fs-id1167836598355\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(15x{y}^{}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span> 15<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span> \\(6{x}^{2}-3xy+4x-2y+{y}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span> \\(10p-9q\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d4<\/span> \\({m}^{4}+4{m}^{3}+6{m}^{2}+4m+1\\)<\/div><\/div><p id=\"fs-id1167829718398\"><strong data-effect=\"bold\">Add and Subtract Polynomials<\/strong><\/p><p id=\"fs-id1167829718404\">In the following exercises, add or subtract the monomials.<\/p><div data-type=\"exercise\" id=\"fs-id1167829808015\"><div data-type=\"problem\" id=\"fs-id1167829808017\"><p id=\"fs-id1167829808019\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\({\\phantom{\\rule{0.2em}{0ex}}\\text{7x}}^{\\text{2}}+5{x}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(\\phantom{\\rule{0.2em}{0ex}}\\text{4a}-9a\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836548593\"><p id=\"fs-id1167836548595\"><span class=\"token\">\u24d0<\/span>\\({\\text{12x}}^{\\text{2}}\\)<span class=\"token\">\u24d1<\/span>\\(\\text{\u2212}\\phantom{\\rule{0.2em}{0ex}}\\text{5a}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829627667\"><div data-type=\"problem\" id=\"fs-id1167829627669\"><p id=\"fs-id1167829627671\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\({\\phantom{\\rule{0.2em}{0ex}}\\text{4y}}^{\\text{3}}+6{y}^{3}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(\\text{\u2212}y-5y\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826205230\"><div data-type=\"problem\" id=\"fs-id1167826205232\"><p id=\"fs-id1167826205234\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(-12w+18w\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(7{x}^{2}y-\\left(-12{x}^{2}y\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836660180\"><p id=\"fs-id1167836660182\"><span class=\"token\">\u24d0<\/span>\\(\\text{6}w\\)<span class=\"token\">\u24d1<\/span>\\(19{x}^{2}y\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836449588\"><div data-type=\"problem\" id=\"fs-id1167836449590\"><p id=\"fs-id1167836449592\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(-3m+9m\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(15y{z}^{2}-\\left(-8y{z}^{2}\\right)\\)<\/div><\/div><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167836621814\"><p id=\"fs-id1167836621816\">\\({\\phantom{\\rule{0.2em}{0ex}}\\text{7x}}^{\\text{2}}+5{x}^{2}+\\phantom{\\rule{0.2em}{0ex}}\\text{4a}-9a\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829746749\"><p id=\"fs-id1167829746751\">\\({\\text{12x}}^{\\text{2}}-\\phantom{\\rule{0.2em}{0ex}}\\text{5a}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833274103\"><div data-type=\"problem\" id=\"fs-id1167833274105\"><p id=\"fs-id1167833274108\">\\({\\phantom{\\rule{0.2em}{0ex}}\\text{4y}}^{\\text{3}}+6{y}^{3}-y-5y\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833023422\"><div data-type=\"problem\" id=\"fs-id1167833023425\"><p id=\"fs-id1167833023427\">\\(-12w+18w+7{x}^{2}y-\\left(-12{x}^{2}y\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829906656\"><p id=\"fs-id1167829906658\">\\(6w+19{x}^{2}y\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833021002\"><div data-type=\"problem\" id=\"fs-id1167833021004\"><p id=\"fs-id1167833021007\">\\(-3m+9m+15y{z}^{2}-\\left(-8y{z}^{2}\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833021640\"><div data-type=\"problem\" id=\"fs-id1167833021642\"><p id=\"fs-id1167833021644\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(-5b-17b\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(3xy-\\left(-8xy\\right)+5xy\\)<\/div><div data-type=\"solution\" id=\"fs-id1167836789251\"><p id=\"fs-id1167836789253\"><span class=\"token\">\u24d0<\/span>\\(-22b\\)<span class=\"token\">\u24d1<\/span>\\(16xy\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836615678\"><div data-type=\"problem\" id=\"fs-id1167836615680\"><p id=\"fs-id1167836615683\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(-10x-35x\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(17m{n}^{2}-\\left(-9m{n}^{2}\\right)+3m{n}^{2}\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836756594\"><div data-type=\"problem\" id=\"fs-id1167836756596\"><p id=\"fs-id1167836756598\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(\\phantom{\\rule{0.2em}{0ex}}\\text{12}a+5b-22a\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(p{q}^{2}-4p-3{q}^{2}\\)<\/div><div data-type=\"solution\" id=\"fs-id1167832925638\"><p id=\"fs-id1167832925640\"><span class=\"token\">\u24d0<\/span>\\(-10a+5b\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(p{q}^{2}-4p-3{q}^{2}\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836492076\"><div data-type=\"problem\" id=\"fs-id1167836492078\"><p id=\"fs-id1167836492080\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(\\phantom{\\rule{0.2em}{0ex}}\\text{14x}-3y-13x\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\({a}^{2}b-4a-5a{b}^{2}\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832936422\"><div data-type=\"problem\" id=\"fs-id1167832936424\"><p id=\"fs-id1167832936426\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(2{a}^{2}+{b}^{2}-6{a}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\({x}^{2}y-3x+7x{y}^{2}\\)<\/div><div data-type=\"solution\" id=\"fs-id1167833060532\"><p id=\"fs-id1167836552096\"><span class=\"token\">\u24d0<\/span>\\(-4{a}^{2}+{b}^{2}\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\({x}^{2}y-3x+7x{y}^{2}\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836440002\"><div data-type=\"problem\" id=\"fs-id1167836440004\"><p id=\"fs-id1167836440006\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(5{u}^{2}+4{v}^{2}-6{u}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(\\phantom{\\rule{0.2em}{0ex}}\\text{12a}+8b\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836596888\"><div data-type=\"problem\" id=\"fs-id1167836596890\"><p id=\"fs-id1167836596892\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>\\(x{y}^{2}-5x-5{y}^{2}\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(\\phantom{\\rule{0.2em}{0ex}}\\text{19y}+5z\\)<\/div><div data-type=\"solution\" id=\"fs-id1167829930529\"><p id=\"fs-id1167829930531\"><span class=\"token\">\u24d0<\/span>\\(x{y}^{2}-5x-5{y}^{2}\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(19y+5z\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836508704\"><div data-type=\"problem\" id=\"fs-id1167836508706\"><p id=\"fs-id1167836508708\">\\(\\text{12}a+5b-22a+p{q}^{2}-4p-3{q}^{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836406955\"><div data-type=\"problem\" id=\"fs-id1167836406957\"><p id=\"fs-id1167836406959\">\\(\\text{14x}-3y-13x+{a}^{2}b-4a-5a{b}^{2}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836434024\"><p id=\"fs-id1167836434026\">\\(x-3y+{a}^{2}b-4a-5a{b}^{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836432063\"><div data-type=\"problem\" id=\"fs-id1167836423784\"><p id=\"fs-id1167836423787\">\\(2{a}^{2}+{b}^{2}-6{a}^{2}+{x}^{2}y-3x+7x{y}^{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829747886\"><div data-type=\"problem\" id=\"fs-id1167829747888\"><p id=\"fs-id1167829747890\">\\(5{u}^{2}+4{v}^{2}-6{u}^{2}+\\phantom{\\rule{0.2em}{0ex}}\\text{12a}+8b\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836409558\"><p id=\"fs-id1167836620844\">\\(\\text{\u2212}{u}^{2}+4{v}^{2}+\\phantom{\\rule{0.2em}{0ex}}\\text{12a}+8b\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836292513\"><div data-type=\"problem\" id=\"fs-id1167836292515\"><p id=\"fs-id1167836737848\">\\(x{y}^{2}-5x-5{y}^{2}+\\phantom{\\rule{0.2em}{0ex}}\\text{19y}+5z\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833338729\"><div data-type=\"problem\" id=\"fs-id1167833338731\"><p id=\"fs-id1167833338733\">Add: \\(4a,-3b,-8a\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832982010\"><p id=\"fs-id1167832982012\">\\(\\text{\u2212}\\text{4a}-3b\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829712496\"><div data-type=\"problem\" id=\"fs-id1167829712498\"><p id=\"fs-id1167829712501\">Add:\\(\\phantom{\\rule{0.2em}{0ex}}\\text{4x},3y,-3x\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833086506\"><div data-type=\"problem\" id=\"fs-id1167833086508\"><p id=\"fs-id1167836429801\">Subtract \\(5{x}^{6}\\) from \\(-12{x}^{6}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167826025484\"><p id=\"fs-id1167826025486\">\\(-7{x}^{6}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826025500\"><div data-type=\"problem\" id=\"fs-id1167833197293\"><p id=\"fs-id1167833197295\">Subtract \\(2{p}^{4}\\) from \\(-7{p}^{4}\\)<\/p><\/div><\/div><p id=\"fs-id1167824733268\">In the following exercises, add the polynomials.<\/p><div data-type=\"exercise\" id=\"fs-id1167824733271\"><div data-type=\"problem\" id=\"fs-id1167824733273\"><p id=\"fs-id1167824733275\">\\(\\left(5{y}^{2}+12y+4\\right)+\\left(6{y}^{2}-8y+7\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836665099\"><p id=\"fs-id1167836665101\">\\(11{y}^{2}+4y+11\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829690282\"><div data-type=\"problem\" id=\"fs-id1167829690285\"><p id=\"fs-id1167829690287\">\\(\\left(4{y}^{2}+10y+3\\right)+\\left(8{y}^{2}-6y+5\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833350072\"><div data-type=\"problem\" id=\"fs-id1167833350074\"><p id=\"fs-id1167833350076\">\\(\\left({x}^{2}+6x+8\\right)+\\left(-4{x}^{2}+11x-9\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836732159\"><p id=\"fs-id1167836732161\">\\(-3{x}^{2}+17x-1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829597471\"><div data-type=\"problem\" id=\"fs-id1167829597473\"><p id=\"fs-id1167829597475\">\\(\\left({y}^{2}+9y+4\\right)+\\left(-2{y}^{2}-5y-1\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836356307\"><div data-type=\"problem\"><p id=\"fs-id1167836456215\">\\(\\left(8{x}^{2}-5x+2\\right)+\\left(3{x}^{2}+3\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833386390\"><p id=\"fs-id1167833386392\">\\(11{x}^{2}-5x+5\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833128238\"><div data-type=\"problem\" id=\"fs-id1167833128240\"><p id=\"fs-id1167829788193\">\\(\\left(7{x}^{2}-9x+2\\right)+\\left(6{x}^{2}-4\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836561092\"><div data-type=\"problem\" id=\"fs-id1167836561095\"><p id=\"fs-id1167836561097\">\\(\\left(5{a}^{2}+8\\right)+\\left({a}^{2}-4a-9\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833385974\"><p id=\"fs-id1167833385976\">\\(6{a}^{2}-4a-1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829844347\"><div data-type=\"problem\" id=\"fs-id1167829844349\"><p id=\"fs-id1167829844351\">\\(\\left({p}^{2}-6p-18\\right)+\\left(2{p}^{2}+11\\right)\\)<\/p><\/div><\/div><p id=\"fs-id1167833142618\">In the following exercises, subtract the polynomials.<\/p><div data-type=\"exercise\" id=\"fs-id1167833142621\"><div data-type=\"problem\" id=\"fs-id1167833142624\"><p id=\"fs-id1167833142626\">\\(\\left(4{m}^{2}-6m-3\\right)-\\left(2{m}^{2}+m-7\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829751095\"><p id=\"fs-id1167836508167\">\\(2{m}^{2}-7m+4\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836398826\"><div data-type=\"problem\"><p>\\(\\left(3{b}^{2}-4b+1\\right)-\\left(5{b}^{2}-b-2\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829834036\"><div data-type=\"problem\" id=\"fs-id1167829834038\"><p id=\"fs-id1167829834041\">\\(\\left({a}^{2}+8a+5\\right)-\\left({a}^{2}-3a+2\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829621172\"><p id=\"fs-id1167829621175\">\\(11a+3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829790417\"><div data-type=\"problem\" id=\"fs-id1167829790419\"><p id=\"fs-id1167829790421\">\\(\\left({b}^{2}-7b+5\\right)-\\left({b}^{2}-2b+9\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836386461\"><div data-type=\"problem\" id=\"fs-id1167830096219\"><p id=\"fs-id1167830096222\">\\(\\left(12{s}^{2}-15s\\right)-\\left(s-9\\right)\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167829907673\">\\(12{s}^{2}-14s+9\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836423564\"><div data-type=\"problem\" id=\"fs-id1167836423566\"><p id=\"fs-id1167836423568\">\\(\\left(10{r}^{2}-20r\\right)-\\left(r-8\\right)\\)<\/p><\/div><\/div><p id=\"fs-id1167829696661\">In the following exercises, subtract the polynomials.<\/p><div data-type=\"exercise\" id=\"fs-id1167829696664\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829696666\"><p id=\"fs-id1167829696668\">Subtract \\(\\left(9{x}^{2}+2\\right)\\) from \\(\\left(12{x}^{2}-x+6\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167824584633\"><p id=\"fs-id1167824584635\">\\(3{x}^{2}-x+4\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829620966\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829620969\"><p id=\"fs-id1167836650171\">Subtract \\(\\left(5{y}^{2}-y+12\\right)\\) from \\(\\left(10{y}^{2}-8y-20\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836613921\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836613923\"><p id=\"fs-id1167836613925\">Subtract \\(\\left(7{w}^{2}-4w+2\\right)\\) from \\(\\left(8{w}^{2}-w+6\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829702031\"><p id=\"fs-id1167829702033\">\\({w}^{2}+3w+4\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836615484\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836615486\"><p id=\"fs-id1167836615488\">Subtract \\(\\left(5{x}^{2}-x+12\\right)\\) from \\(\\left(9{x}^{2}-6x-20\\right)\\)<\/p><\/div><\/div><p id=\"fs-id1167836666634\">In the following exercises, find the difference of the polynomials.<\/p><div data-type=\"exercise\" id=\"fs-id1167829717203\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829717206\"><p id=\"fs-id1167829717208\">Find the difference of \\(\\left({w}^{2}+w-42\\right)\\) and \\(\\left({w}^{2}-10w+24\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167829589207\"><p id=\"fs-id1167829589209\">\\(11w-64\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836531012\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836531014\"><p id=\"fs-id1167836531017\">Find the difference of \\(\\left({z}^{2}-3z-18\\right)\\) and \\(\\left({z}^{2}+5z-20\\right)\\)<\/p><\/div><\/div><p id=\"fs-id1167829931386\">In the following exercises, add the polynomials.<\/p><div data-type=\"exercise\" id=\"fs-id1167829931390\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829931392\"><p id=\"fs-id1167829931394\">\\(\\left(7{x}^{2}-2xy+6{y}^{2}\\right)+\\left(3{x}^{2}-5xy\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836596754\"><p id=\"fs-id1167832981645\">\\(10{x}^{2}-7xy+6{y}^{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836728252\"><p id=\"fs-id1167836728254\">\\(\\left(-5{x}^{2}-4xy-3{y}^{2}\\right)+\\left(2{x}^{2}-7xy\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824740668\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167824740670\"><p id=\"fs-id1167824740672\">\\(\\left(7{m}^{2}+mn-8{n}^{2}\\right)+\\left(3{m}^{2}+2mn\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836407251\"><p id=\"fs-id1167836484935\">\\(10{m}^{2}+3mn-8{n}^{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836423638\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836423640\"><p id=\"fs-id1167836423642\">\\(\\left(2{r}^{2}-3rs-2{s}^{2}\\right)+\\left(5{r}^{2}-3rs\\right)\\)<\/p><\/div><\/div><p id=\"fs-id1167829742745\">In the following exercises, add or subtract the polynomials.<\/p><div data-type=\"exercise\" id=\"fs-id1167829742748\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829742751\"><p id=\"fs-id1167829742753\">\\(\\left({a}^{2}-{b}^{2}\\right)-\\left({a}^{2}+3ab-4{b}^{2}\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833086321\"><p id=\"fs-id1167833086323\">\\(-3ab+3{b}^{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829787220\"><p id=\"fs-id1167829787222\">\\(\\left({m}^{2}+2{n}^{2}\\right)-\\left({m}^{2}-8mn-{n}^{2}\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829594307\" class=\"material-set-2\"><div data-type=\"problem\"><p>\\(\\left({p}^{3}-3{p}^{2}q\\right)+\\left(2p{q}^{2}+4{q}^{3}\\right)-\\left(3{p}^{2}q+p{q}^{2}\\right)\\)<\/p><\/div><div data-type=\"solution\"><p>\\({p}^{3}-6{p}^{2}q+p{q}^{2}+4{q}^{3}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829750509\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829750511\"><p id=\"fs-id1167829750513\">\\(\\left({a}^{3}-2{a}^{2}b\\right)+\\left(a{b}^{2}+{b}^{3}\\right)-\\left(3{a}^{2}b+4a{b}^{2}\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829905295\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829905297\"><p id=\"fs-id1167829905299\">\\(\\left({x}^{3}-{x}^{2}y\\right)-\\left(4x{y}^{2}-{y}^{3}\\right)+\\left(3{x}^{2}y-x{y}^{2}\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836599533\"><p id=\"fs-id1167836599535\">\\({x}^{3}+2{x}^{2}y-5x{y}^{2}+{y}^{3}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836629436\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836629438\"><p id=\"fs-id1167836629440\">\\(\\left({x}^{3}-2{x}^{2}y\\right)-\\left(x{y}^{2}-3{y}^{3}\\right)-\\left({x}^{2}y-4x{y}^{2}\\right)\\)<\/p><\/div><\/div><p id=\"fs-id1167836432779\"><strong data-effect=\"bold\">Evaluate a Polynomial Function for a Given Value<\/strong><\/p><p id=\"fs-id1167836432784\">In the following exercises, find the function values for each polynomial function.<\/p><div data-type=\"exercise\" id=\"fs-id1167836432788\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836432790\"><p>For the function \\(f\\left(x\\right)=8{x}^{2}-3x+2,\\) find:<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(f\\left(5\\right)\\) <span class=\"token\">\u24d1<\/span> \\(f\\left(-2\\right)\\) <span class=\"token\">\u24d2<\/span> \\(f\\left(0\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167832982231\"><p id=\"fs-id1167832982233\"><span class=\"token\">\u24d0<\/span> 187 <span class=\"token\">\u24d1<\/span> 40 <span class=\"token\">\u24d2<\/span> 2<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832982250\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167832982252\"><p id=\"fs-id1167836561341\">For the function \\(f\\left(x\\right)=5{x}^{2}-x-7,\\) find:<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(f\\left(-4\\right)\\) <span class=\"token\">\u24d1<\/span> \\(f\\left(1\\right)\\) <span class=\"token\">\u24d2<\/span> \\(f\\left(0\\right)\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167829738632\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829738634\"><p id=\"fs-id1167829738637\">For the function \\(g\\left(x\\right)=4-36x,\\) find:<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(g\\left(3\\right)\\) <span class=\"token\">\u24d1<\/span> \\(g\\left(0\\right)\\) <span class=\"token\">\u24d2<\/span> \\(g\\left(-1\\right)\\)<\/div><div data-type=\"solution\" id=\"fs-id1167832977153\"><p id=\"fs-id1167832977155\"><span class=\"token\">\u24d0<\/span>\\(-104\\)<span class=\"token\">\u24d1<\/span> 4 <span class=\"token\">\u24d2<\/span> 40<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836558053\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836558055\"><p id=\"fs-id1167836558057\">For the function \\(g\\left(x\\right)=16-36{x}^{2},\\) find:<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span> \\(g\\left(-1\\right)\\) <span class=\"token\">\u24d1<\/span> \\(g\\left(0\\right)\\) <span class=\"token\">\u24d2<\/span> \\(g\\left(2\\right)\\)<\/div><\/div><p id=\"fs-id1167824754903\">In the following exercises, find the height for each polynomial function.<\/p><div data-type=\"exercise\" id=\"fs-id1167836609191\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836609193\"><p id=\"fs-id1167836609196\">A painter drops a brush from a platform 75 feet high. The polynomial function \\(h\\left(t\\right)=-16{t}^{2}+75\\) gives the height of the brush <em data-effect=\"italics\">t<\/em> seconds after it was dropped. Find the height after \\(t=2\\) seconds.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836423697\"><p id=\"fs-id1167836423699\">The height is 11 feet.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836333432\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836333434\"><p id=\"fs-id1167836333436\">A girl drops a ball off the cliff into the ocean. The polynomial \\(h\\left(t\\right)=-16{t}^{2}+200\\) gives the height of a ball <em data-effect=\"italics\">t<\/em> seconds after it is dropped. Find the height after \\(t=3\\) seconds.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824755607\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167824755609\"><p id=\"fs-id1167824755611\">A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of <em data-effect=\"italics\">p<\/em> dollars each is given by the polynomial function \\(R\\left(p\\right)=-4{p}^{2}+420p.\\) Find the revenue received when \\(p=60\\) dollars.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836732114\"><p id=\"fs-id1167836732116\">The revenue is ?10,800.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836732122\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836732124\"><p id=\"fs-id1167836732126\">A manufacturer of the latest basketball shoes has found that the revenue received from selling the shoes at a cost of <em data-effect=\"italics\">p<\/em> dollars each is given by the polynomial \\(R\\left(p\\right)=-4{p}^{2}+420p.\\) Find the revenue received when \\(p=90\\) dollars.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833022467\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833022469\"><p id=\"fs-id1167833022472\">The polynomial \\(C\\left(x\\right)=6{x}^{2}+90x\\) gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side <em data-effect=\"italics\">x<\/em> feet and height 6 feet. Find the cost of producing a box with \\(x=4\\) feet.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833050568\"><p id=\"fs-id1167833050570\">The cost is ?456.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833050575\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167829695828\"><p id=\"fs-id1167829695830\">The polynomial \\(C\\left(x\\right)=6{x}^{2}+90x\\) gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side <em data-effect=\"italics\">x<\/em> feet and height 4 feet. Find the cost of producing a box with \\(x=6\\) feet.<\/p><\/div><\/div><p id=\"fs-id1167833381677\"><strong data-effect=\"bold\">Add and Subtract Polynomial Functions<\/strong><\/p><p id=\"fs-id1167833381682\">In each example, find <span class=\"token\">\u24d0<\/span> (<em data-effect=\"italics\">f<\/em> + <em data-effect=\"italics\">g<\/em>)(<em data-effect=\"italics\">x<\/em>)\u2003<span class=\"token\">\u24d1<\/span> (<em data-effect=\"italics\">f<\/em> + <em data-effect=\"italics\">g<\/em>)(2)\u2003<span class=\"token\">\u24d2<\/span> (<em data-effect=\"italics\">f<\/em> \u2212 <em data-effect=\"italics\">g<\/em>)(<em data-effect=\"italics\">x<\/em>)\u2003<span class=\"token\">\u24d3<\/span> (<em data-effect=\"italics\">f<\/em> \u2212 <em data-effect=\"italics\">g<\/em>)(\u22123).<\/p><div data-type=\"exercise\" id=\"fs-id1167836418844\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836418846\"><p id=\"fs-id1167836418848\">\\(f\\left(x\\right)=2{x}^{2}-4x+1\\) and \\(g\\left(x\\right)=5{x}^{2}+8x+3\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167833086694\"><p id=\"fs-id1167833086696\"><span class=\"token\">\u24d0<\/span>\\(\\left(f+g\\right)\\left(x\\right)=7{x}^{2}+4x+4\\)<span class=\"token\">\u24d1<\/span>\\(\\left(f+g\\right)\\left(2\\right)=40\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(f-g\\right)\\left(x\\right)=-3{x}^{2}-12x-2\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span>\\(\\left(f-g\\right)\\left(-3\\right)=7\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167833347303\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167833347305\"><p id=\"fs-id1167833347308\">\\(f\\left(x\\right)=4{x}^{2}-7x+3\\) and \\(g\\left(x\\right)=4{x}^{2}+2x-1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836624045\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167836624047\"><p id=\"fs-id1167836624049\">\\(f\\left(x\\right)=3{x}^{3}-{x}^{2}-2x+3\\) and \\(g\\left(x\\right)=3{x}^{3}-7x\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836409394\"><p id=\"fs-id1167836409396\"><\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d0<\/span>&nbsp;\\(\\left(f+g\\right)\\left(x\\right)=6{x}^{3}-{x}^{2}-9x+3\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(\\left(f+g\\right)\\left(2\\right)=29\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d2<\/span>\\(\\left(f-g\\right)\\left(x\\right)=\\text{\u2212}{x}^{2}+5x+3\\)<div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d3<\/span>\\(\\left(f-g\\right)\\left(-3\\right)=-21\\)<\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824732288\" class=\"material-set-2\"><div data-type=\"problem\" id=\"fs-id1167824732290\"><p id=\"fs-id1167824732292\">\\(f\\left(x\\right)=5{x}^{3}-{x}^{2}+3x+4\\) and \\(g\\left(x\\right)=8{x}^{3}-1\\)<\/p><\/div><\/div><\/div><div class=\"writing\" data-depth=\"2\" id=\"fs-id1167836529231\"><h4 data-type=\"title\">Writing Exercises<\/h4><div data-type=\"exercise\" id=\"fs-id1167836529238\"><div data-type=\"problem\" id=\"fs-id1167836529240\"><p id=\"fs-id1167836529242\">Using your own words, explain the difference between a monomial, a binomial, and a trinomial.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836529248\"><p id=\"fs-id1167836529250\">Answers will vary.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167836529255\"><div data-type=\"problem\" id=\"fs-id1167836618900\"><p id=\"fs-id1167836618902\">Using your own words, explain the difference between a polynomial with five terms and a polynomial with a degree of 5.<\/p><\/div><\/div><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167836618917\"><p id=\"fs-id1167836618919\">Ariana thinks the sum \\(6{y}^{2}+5{y}^{4}\\) is \\(11{y}^{6}.\\) What is wrong with her reasoning?<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167836494401\"><p id=\"fs-id1167836494403\">Answers will vary.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167824755444\"><div data-type=\"problem\" id=\"fs-id1167824755447\"><p id=\"fs-id1167824755449\">Is every trinomial a second degree polynomial? If not, give an example.<\/p><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167824755462\"><h4 data-type=\"title\">Self Check<\/h4><p id=\"fs-id1167824755467\"><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p><span data-type=\"media\" id=\"fs-id1167836602621\" data-alt=\"The figure shows a table with six rows and four columns. The first row is a header row and it labels each column. The first column header is \u201cI can\u2026\u201d, the second is &quot;confidently&quot;, the third is \u201cwith some help\u201d, \u201cno minus I don\u2019t get it!\u201d. Under the first column are the phrases \u201cidentify polynomials, monomials, binomials, and trinomials\u201d, \u201cdetermine the degree of polynomials\u201d, \u201cadd and subtract monomials\u201d, \u201cadd and subtract polynomials\u201d, and \u201cevaluate a polynomial for a given value\u201d. Under the second, third, fourth columns are blank spaces where the learner can check what level of mastery they have achieved.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_201_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a table with six rows and four columns. The first row is a header row and it labels each column. The first column header is \u201cI can\u2026\u201d, the second is &quot;confidently&quot;, the third is \u201cwith some help\u201d, \u201cno minus I don\u2019t get it!\u201d. Under the first column are the phrases \u201cidentify polynomials, monomials, binomials, and trinomials\u201d, \u201cdetermine the degree of polynomials\u201d, \u201cadd and subtract monomials\u201d, \u201cadd and subtract polynomials\u201d, and \u201cevaluate a polynomial for a given value\u201d. Under the second, third, fourth columns are blank spaces where the learner can check what level of mastery they have achieved.\"><\/span><p id=\"fs-id1167836602631\"><span class=\"token\">\u24d1<\/span> If most of your checks were:<\/p><p id=\"fs-id1167836602638\"><strong data-effect=\"bold\">\u2026confidently.<\/strong> Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.<\/p><p id=\"fs-id1167829767167\"><strong data-effect=\"bold\">\u2026with some help.<\/strong> This must be addressed quickly because topics you do not master become potholes in your road to success. In math every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?<\/p><p id=\"fs-id1167829767178\"><strong data-effect=\"bold\">\u2026no - I don\u2019t get it!<\/strong> This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.<\/p><\/div><\/div><div data-type=\"glossary\" class=\"textbox shaded\"><h3 data-type=\"glossary-title\">Glossary<\/h3><dl id=\"fs-id1167836508735\"><dt>binomial<\/dt><dd id=\"fs-id1167836508741\">A binomial is a polynomial with exactly two terms.<\/dd><\/dl><dl id=\"fs-id1167836508745\"><dt>degree of a constant<\/dt><dd id=\"fs-id1167836508750\">The degree of any constant is 0.<\/dd><\/dl><dl id=\"fs-id1167836508755\"><dt>degree of a polynomial<\/dt><dd id=\"fs-id1167836508760\">The degree of a polynomial is the highest degree of all its terms.<\/dd><\/dl><dl id=\"fs-id1167836508764\"><dt>degree of a term<\/dt><dd id=\"fs-id1167833385664\">The degree of a term is the sum of the exponents of its variables.<\/dd><\/dl><dl id=\"fs-id1167833385668\"><dt>monomial<\/dt><dd id=\"fs-id1167833385674\">A monomial is an algebraic expression with one term. A monomial in one variable is a term of the form \\(a{x}^{m},\\) where <em data-effect=\"italics\">a<\/em> is a constant and <em data-effect=\"italics\">m<\/em> is a whole number.<\/dd><\/dl><dl id=\"fs-id1167829853744\"><dt>polynomial<\/dt><dd id=\"fs-id1167829853749\">A monomial or two or more monomials combined by addition or subtraction is a polynomial.<\/dd><\/dl><dl id=\"fs-id1167829853754\"><dt>standard form of a polynomial<\/dt><dd id=\"fs-id1167829853760\">A polynomial is in standard form when the terms of a polynomial are written in descending order of degrees.<\/dd><\/dl><dl id=\"fs-id1167833350539\"><dt>trinomial<\/dt><dd id=\"fs-id1167833350544\">A trinomial is a polynomial with exactly three terms.<\/dd><\/dl><dl id=\"fs-id1167833350548\"><dt>polynomial function<\/dt><dd id=\"fs-id1167833350554\">A polynomial function is a function whose range values are defined by a polynomial.<\/dd><\/dl><\/div>\n","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to: <\/p>\n<ul>\n<li>Determine the degree of polynomials<\/li>\n<li>Add and subtract polynomials<\/li>\n<li>Evaluate a polynomial function for a given value<\/li>\n<li>Add and subtract polynomial functions<\/li>\n<\/ul>\n<\/div>\n<div data-type=\"note\" class=\"be-prepared\">\n<p>Before you get started, take this readiness quiz.<\/p>\n<ol id=\"fs-id1167836415169\" type=\"1\">\n<li>Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e4acb5c267eccb67777d4bcbd32c918d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#43;&#49;&#43;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#43;&#53;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"222\" style=\"vertical-align: -2px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167836652573\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>Subtract: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a1e582a4e5ceb9ac1cbd54444691af83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#110;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"155\" style=\"vertical-align: -4px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p>If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167829586631\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>Evaluate: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cf4181c640b70891bfa863177f5aa2cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"35\" style=\"vertical-align: -4px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-01f282abd343bbe6b83c45e54b86c6ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cf6f0342bc735be628e5e6062a1a2a19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"46\" style=\"vertical-align: -4px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/05eab039-6d1c-4d80-8c8c-94469164a52c#fs-id1167832053133\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<\/ol>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836299901\">\n<h3 data-type=\"title\">Determine the Degree of Polynomials<\/h3>\n<p id=\"fs-id1167836319331\">We have learned that a <em data-effect=\"italics\">term<\/em> is a constant or the product of a constant and one or more variables. A <span data-type=\"term\">monomial<\/span> is an algebraic expression with one term. When it is of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f8fe74b3bd004d025e1a2dce9b428a1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#123;&#120;&#125;&#94;&#123;&#109;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"36\" style=\"vertical-align: -4px;\" \/> where <em data-effect=\"italics\">a<\/em> is a constant and <em data-effect=\"italics\">m<\/em> is a whole number, it is called a monomial in one variable. Some examples of monomial in one variable are. Monomials can also have more than one variable such as and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-784f69c11010b1d3825517c4afc72a94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -1px;\" \/><\/p>\n<div data-type=\"note\">\n<div data-type=\"title\">Monomial<\/div>\n<p id=\"fs-id1167824734983\">A <strong data-effect=\"bold\">monomial<\/strong> is an algebraic expression with one term.<\/p>\n<p id=\"fs-id1167836409519\">A monomial in one variable is a term of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f8fe74b3bd004d025e1a2dce9b428a1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#123;&#120;&#125;&#94;&#123;&#109;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"36\" style=\"vertical-align: -4px;\" \/> where <em data-effect=\"italics\">a<\/em> is a constant and <em data-effect=\"italics\">m<\/em> is a whole number.<\/p>\n<\/div>\n<p id=\"fs-id1167833023042\">A monomial, or two or more monomials combined by addition or subtraction, is a <span data-type=\"term\">polynomial<\/span>. Some polynomials have special names, based on the number of terms. A monomial is a polynomial with exactly one term. A binomial has exactly two terms, and a <span data-type=\"term\">trinomial<\/span> has exactly three terms. There are no special names for polynomials with more than three terms.<\/p>\n<div data-type=\"note\" id=\"fs-id1167829688772\">\n<div data-type=\"title\">Polynomials<\/div>\n<p id=\"fs-id1167836481441\"><strong data-effect=\"bold\">polynomial<\/strong>\u2014A monomial, or two or more algebraic terms combined by addition or subtraction is a polynomial.<\/p>\n<p id=\"fs-id1167829628029\"><strong data-effect=\"bold\">monomial<\/strong>\u2014A polynomial with exactly one term is called a monomial.<\/p>\n<p id=\"fs-id1167829720442\"><strong data-effect=\"bold\">binomial<\/strong>\u2014A polynomial with exactly two terms is called a binomial.<\/p>\n<p id=\"fs-id1167836510464\"><strong data-effect=\"bold\">trinomial<\/strong>\u2014A polynomial with exactly three terms is called a trinomial.<\/p>\n<\/div>\n<p id=\"fs-id1167836349269\">Here are some examples of polynomials.<\/p>\n<table id=\"fs-id1167829661616\" class=\"unnumbered\" summary=\"This table has five columns and four rows. The first row is for polynomials and lists three examples: y plus 1, 4 a squared minus 7 a b plus 2 b squared, 4 x to the fourth power plus x cubed plus 8 x squared minus 9 x plus 1. The second row is for monomials and lists four examples: 14, 8 y squared, minus 9 x cubed y to the fifth power, and negative 12 a cubed b squared c. The third row is for binomials and lists four examples: a plus 7 b, 4 x square minus y squared, y squared minus 16, and 3 p cubed q minus 9 p squared q. The fourth row is for trinomials and list four examples: x squared minus 7 x plus 12, 9 m squared plus 2 mn minus 8 n squared, 6 k to the fourth power minus k cubed plus 8 k, and z to the fourth power plus 3z squared minus 1.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Polynomial<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a0369eb2f2cdc0e7f35e84bca4ae50c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"39\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ec9ddc40db44e77b16927b20da4d6708_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#97;&#98;&#43;&#50;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"119\" style=\"vertical-align: -2px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9076651bcf6c38dcadc7b2a49e4ed159_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#43;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"185\" style=\"vertical-align: -2px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Monomial<\/td>\n<td data-valign=\"top\" data-align=\"left\">14<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-649c835f6f65cf7f7c974a270b0c159b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-91f32fd1aa875ce4c9a7cca4be6577ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-87271bea20f30442ed148a0cdfc19d48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#51;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"71\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Binomial<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2425787df2830232a35c57f45350a5df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#55;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: -2px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2543f38cecf767faed7524c75f4b650f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c86ed2cc63da68d2aa72da9b5992f3c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-62480218c30eaae001f0f7230d5c34e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#113;&#45;&#57;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Trinomial<\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3aab27973cf8e4725f634de4c1e50bb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#120;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"97\" style=\"vertical-align: -2px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-123b31e3c4e547514023c8b09862aa91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#109;&#110;&#45;&#56;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"138\" style=\"vertical-align: -2px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3ca23aa464dde9a8f57c49524760ed86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#107;&#125;&#94;&#123;&#52;&#125;&#45;&#123;&#107;&#125;&#94;&#123;&#51;&#125;&#43;&#56;&#107;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -2px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bca3d90d9c8073c07704e05f316040d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#52;&#125;&#43;&#51;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"94\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that every monomial, binomial, and trinomial is also a polynomial. They are just special members of the \u201cfamily\u201d of polynomials and so they have special names. We use the words <em data-effect=\"italics\">monomial<\/em>, <em data-effect=\"italics\">binomial<\/em>, and <em data-effect=\"italics\">trinomial<\/em> when referring to these special polynomials and just call all the rest <em data-effect=\"italics\">polynomials<\/em>.<\/p>\n<p id=\"fs-id1167836298253\">The <span data-type=\"term\">degree of a polynomial<\/span> and the degree of its terms are determined by the exponents of the variable.<\/p>\n<p id=\"fs-id1167836322222\">A monomial that has no variable, just a constant, is a special case. The <span data-type=\"term\">degree of a constant<\/span> is 0.<\/p>\n<div data-type=\"note\" id=\"fs-id1167836310024\">\n<div data-type=\"title\">Degree of a Polynomial<\/div>\n<p>The <strong data-effect=\"bold\">degree of a term<\/strong> is the sum of the exponents of its variables.<\/p>\n<p>The <strong data-effect=\"bold\">degree of a constant<\/strong> is 0.<\/p>\n<p>The <strong data-effect=\"bold\">degree of a polynomial<\/strong> is the highest degree of all its terms.<\/p>\n<\/div>\n<p>Let\u2019s see how this works by looking at several polynomials. We\u2019ll take it step by step, starting with monomials, and then progressing to polynomials with more terms.<\/p>\n<p id=\"fs-id1167836628336\">Let&#8217;s start by looking at a monomial. The monomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ec3ad513f9937743f9df9cb0872ba651_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"33\" style=\"vertical-align: 0px;\" \/> has two variables <em data-effect=\"italics\">a<\/em> and <em data-effect=\"italics\">b<\/em>. To find the degree we need to find the sum of the exponents. The variable a doesn&#8217;t have an exponent written, but remember that means the exponent is 1. The exponent of <em data-effect=\"italics\">b<\/em> is 2. The sum of the exponents, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7d06c305dcef2594f4cecd7494d7bc19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#50;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"43\" style=\"vertical-align: -4px;\" \/> is 3 so the degree is 3.<\/p>\n<p><span data-type=\"media\" data-alt=\"The polynomial is 8 a b squared. The exponents of the variables are 1 and 2 so the degree of the monomial is 1 plus 2 which equals 3.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_001_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The polynomial is 8 a b squared. The exponents of the variables are 1 and 2 so the degree of the monomial is 1 plus 2 which equals 3.\" \/><\/span><\/p>\n<p id=\"fs-id1167836508452\">Here are some additional examples.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167836282723\" data-alt=\"Monomial examples: 14 has degree 0, 8 a b squared has degree 3, negative 9 x cubed y to the fifth power has degree 8, negative 13 a has degree 1. Binomial examples: The terms in h plus 7 have degree 1 and 0 so the degree of the whole polynomial is 1. The terms in 7 b squared minus 3 b have degree 2 and 1 so the degree of the whole polynomial is 2. The terms in z squared y squared minus 25 have degree 4 and 0 so the degree of the whole polynomial is 4. The terms in 4 n cubed minus 8 n squared have degree 3 and 2 so the degree of the whole polynomial is 3. Trinomial examples: The terms in x squared minus 12 x plus 27 have degree 2, 1 and 0 so the degree of the whole polynomial is 2. The terms in 9 a squared plus 6 a b plus b squared have degree 2, 2, and 2 so the degree of the whole polynomial is 2. The terms in 6 m to the fourth power minus m cubed n squared plus 8 m n to the fifth power have degree 4, 5, and 6 so the degree of the whole polynomial is 6. The terms in z to the fourth power plus 3 z squared minus 1 have degree 4, 2, and 0 so the degree of the whole polynomial is 4. Polynomial examples: The terms in y minus 1 have degree 1 and 0 so the degree of the whole polynomial is 1. The terms in 3 y squared minus 2 y minus 5 have degree 2, 1, 0 so the degree of the whole polynomial is 2. The terms in 4 x to the fourth power plus x cubed plus eight x squared minus 9 x plus 1 have degree 4, 3, 2, 1, and 0 so the degree of the whole polynomial is 4.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_002_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Monomial examples: 14 has degree 0, 8 a b squared has degree 3, negative 9 x cubed y to the fifth power has degree 8, negative 13 a has degree 1. Binomial examples: The terms in h plus 7 have degree 1 and 0 so the degree of the whole polynomial is 1. The terms in 7 b squared minus 3 b have degree 2 and 1 so the degree of the whole polynomial is 2. The terms in z squared y squared minus 25 have degree 4 and 0 so the degree of the whole polynomial is 4. The terms in 4 n cubed minus 8 n squared have degree 3 and 2 so the degree of the whole polynomial is 3. Trinomial examples: The terms in x squared minus 12 x plus 27 have degree 2, 1 and 0 so the degree of the whole polynomial is 2. The terms in 9 a squared plus 6 a b plus b squared have degree 2, 2, and 2 so the degree of the whole polynomial is 2. The terms in 6 m to the fourth power minus m cubed n squared plus 8 m n to the fifth power have degree 4, 5, and 6 so the degree of the whole polynomial is 6. The terms in z to the fourth power plus 3 z squared minus 1 have degree 4, 2, and 0 so the degree of the whole polynomial is 4. Polynomial examples: The terms in y minus 1 have degree 1 and 0 so the degree of the whole polynomial is 1. The terms in 3 y squared minus 2 y minus 5 have degree 2, 1, 0 so the degree of the whole polynomial is 2. The terms in 4 x to the fourth power plus x cubed plus eight x squared minus 9 x plus 1 have degree 4, 3, 2, 1, and 0 so the degree of the whole polynomial is 4.\" \/><\/span><\/p>\n<p id=\"fs-id1167836523638\">Working with polynomials is easier when you list the terms in descending order of degrees. When a polynomial is written this way, it is said to be in <span data-type=\"term\">standard form of a polynomial<\/span>. Get in the habit of writing the term with the highest degree first.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836415722\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836529152\">\n<div data-type=\"problem\" id=\"fs-id1167829694957\">\n<p id=\"fs-id1167836546580\">Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial.<\/p>\n<p id=\"fs-id1167836456244\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-af9cd1e9c532132e3f9e50e653c21157_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#121;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b08de882e94944e340d198ecad2a3309_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e030b34ff0b84d434efebf2fdddaee99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#45;&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#120;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"186\" style=\"vertical-align: -2px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e629f7a130017231edb1aea565addd8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#121;&#45;&#56;&#120;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d4<\/span> 15<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836635375\">\n<table id=\"fs-id1167836357312\" class=\"unnumbered\" summary=\"This table has five columns. The first is labeled polynomials, the second is number of terms, the third is type, the fourth is degree of terms, and the fifth is degree of polynomial. The first row shows 7 y squared minus 5y plus 3 has 3 terms, trinomial, the degree of terms are 2, 1, 0, and the degree of the polynomial is 2. The second row shows minus 2 a to the fourth b squared has 1 term, monomial, degree of terms and degree of polynomial are both 4. The third row shows 3 x to the fifth power minus 4 x cubed minus 6 x squared plus x minus 8 has 5 terms, is a polynomial, and the degree of terms are 5, 3, 2, 0, and 1, so the degree of the polynomial is 5. The fourth row shows 2y minus 8 x y cubed has 2 terms, is a binomial, has degree of terms 1 and 5, and the degree of the polynomial is 4. The fifth row shows 14 which has 1 term and is a monomial with degree of terms and degree of polynomial 0.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-valign=\"top\" data-align=\"left\"><\/th>\n<th data-valign=\"top\" data-align=\"left\">Polynomial<\/th>\n<th data-valign=\"top\" data-align=\"left\">Number of terms<\/th>\n<th data-valign=\"top\" data-align=\"left\">Type<\/th>\n<th data-valign=\"top\" data-align=\"left\">Degree of terms<\/th>\n<th data-valign=\"top\" data-align=\"left\">Degree of polynomial<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\"><span class=\"token\">\u24d0<\/span><\/td>\n<td data-valign=\"middle\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-af9cd1e9c532132e3f9e50e653c21157_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#121;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\">3<\/td>\n<td data-valign=\"middle\" data-align=\"left\">Trinomial<\/td>\n<td data-valign=\"middle\" data-align=\"center\">2, 1, 0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\"><span class=\"token\">\u24d1<\/span><\/td>\n<td data-valign=\"middle\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b08de882e94944e340d198ecad2a3309_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"left\">Monomial<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4, 2<\/td>\n<td data-valign=\"middle\" data-align=\"center\">6<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\"><span class=\"token\">\u24d2<\/span><\/td>\n<td data-valign=\"middle\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e030b34ff0b84d434efebf2fdddaee99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#45;&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#120;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"186\" style=\"vertical-align: -2px;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\">5<\/td>\n<td data-valign=\"middle\" data-align=\"left\">Polynomial<\/td>\n<td data-valign=\"middle\" data-align=\"center\">5, 3, 2, 1, 0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">5<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\"><span class=\"token\">\u24d3<\/span><\/td>\n<td data-valign=\"middle\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e629f7a130017231edb1aea565addd8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#121;&#45;&#56;&#120;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"center\">2<\/td>\n<td data-valign=\"middle\" data-align=\"left\">Binomial<\/td>\n<td data-valign=\"middle\" data-align=\"center\">1, 4<\/td>\n<td data-valign=\"middle\" data-align=\"center\">4<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"middle\" data-align=\"left\"><span class=\"token\">\u24d4<\/span><\/td>\n<td data-valign=\"middle\" data-align=\"left\">15<\/td>\n<td data-valign=\"middle\" data-align=\"center\">1<\/td>\n<td data-valign=\"middle\" data-align=\"left\">Monomial<\/td>\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<td data-valign=\"middle\" data-align=\"center\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836518702\">\n<div data-type=\"problem\">\n<p>Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial.<\/p>\n<p id=\"fs-id1167836544732\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7b5b9d9f382b11767d19f257afca0019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0982c66353e8ad1e2e95099cec37fbf3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#55;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#121;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"135\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8354583ab5f1b4b872938005d6b3363f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#45;&#53;&#120;&#121;&#43;&#57;&#120;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"156\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c13d32ca33707fdcb24c88c1e1dfc311_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"90\" style=\"vertical-align: -1px;\" \/><span class=\"token\">\u24d4<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-525570753cbbaa0926a83dc1c8183c18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167836625437\"><span class=\"token\">\u24d0<\/span> monomial, 0<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> polynomial, 3 <span class=\"token\">\u24d2<\/span> trinomial, 3<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span> binomial, 2 <span class=\"token\">\u24d4<\/span> monomial, 10<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836624239\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829751398\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167836552504\">Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial.<\/p>\n<p id=\"fs-id1167836553862\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c6673d13c1e8b347c47c4ae757b9c61c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#52;&#123;&#107;&#125;&#94;&#123;&#51;&#125;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -1px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a0372f36712dc6478e44619c0ab5e285_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#43;&#52;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"116\" style=\"vertical-align: -2px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8b589e486fc233b12d903a213a61a086_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8732825f1a46e761396822ae31438237_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#45;&#55;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#98;&#45;&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#97;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#43;&#55;&#123;&#98;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"245\" style=\"vertical-align: -2px;\" \/><span class=\"token\">\u24d4<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9238b3969d1b78fa773a9bbd6347b9ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#123;&#113;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836574318\">\n<p id=\"fs-id1167829752758\"><span class=\"token\">\u24d0<\/span>binomial, 3 <span class=\"token\">\u24d1<\/span> trinomial, 3 <span class=\"token\">\u24d2<\/span> monomial, 0 <span class=\"token\">\u24d3<\/span> polynomial, 4 <span class=\"token\">\u24d4<\/span> monomial, 7<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\">Add and Subtract Polynomials<\/h3>\n<p id=\"fs-id1167836297171\">We have learned how to simplify expressions by combining like terms. Remember, like terms must have the same variables with the same exponent. Since monomials are terms, adding and subtracting monomials is the same as combining like terms. If the monomials are like terms, we just combine them by adding or subtracting the coefficients.<\/p>\n<div data-type=\"example\" id=\"fs-id1167829908757\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167829589861\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167836295565\">Add or subtract: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f2c5d9e4357230bcf85f71cb7215dcf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"90\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2099cdaa6f938be4f07bb96b86e2abbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#112;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#112;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"135\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836282025\">\n<p id=\"fs-id1167836341558\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d5122ddf656e1933ef3dee70aa7f2812_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#109;&#98;&#105;&#110;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#48;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"348\" style=\"vertical-align: -15px;\" \/><\/p>\n<p id=\"fs-id1167836362982\"><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a88c90e1567ef0ee035618ab2aadda9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#54;&#112;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#112;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#109;&#98;&#105;&#110;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#51;&#112;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"384\" style=\"vertical-align: -15px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836353044\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836390664\">\n<div data-type=\"problem\" id=\"fs-id1167829716743\">\n<p id=\"fs-id1167836392806\">Add or subtract: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6175c0efbb4cc146597e1641e5cc3e25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-47ae1f6f249cfffb26fe0e2faf2e69aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#109;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#109;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"144\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836389469\">\n<p id=\"fs-id1167833345172\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7c4778034779d319d3992f9efa51bd22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-eb75a0dea9830734bace3dfa8af5518a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#109;&#123;&#110;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"51\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836357323\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167833310117\">\n<div data-type=\"problem\" id=\"fs-id1167836693189\">\n<p id=\"fs-id1167836628342\">Add or subtract: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7908277228e54b81a740b4600c86929c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#123;&#99;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"92\" style=\"vertical-align: -2px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-81e05ae9216ac14a9ef078f7cda08bc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#123;&#122;&#125;&#94;&#123;&#51;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#123;&#122;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"166\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836610409\">\n<p id=\"fs-id1167836613592\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3a8269f16cfb6ed51382b54d3564ce6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#123;&#99;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-580cd347019aae7b13b0a7bb28f25f54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#123;&#122;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"64\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836299490\">Remember that like terms must have the same variables with the same exponents.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836700849\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836524855\">\n<div data-type=\"problem\" id=\"fs-id1167836615698\">\n<p>Simplify: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-222a3463b4299363453ff0019c309cac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"110\" style=\"vertical-align: -2px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f8ebfb812cde4dfbc931744d131aa33b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#118;&#43;&#53;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"127\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836692468\">\n<p id=\"fs-id1167836532785\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a9d49ddfbe3d52aeb0fb3b51c853e055_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#57;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#109;&#98;&#105;&#110;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#57;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#53;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"473\" style=\"vertical-align: -13px;\" \/><\/p>\n<p><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-67974f4bf6ea30f488ebfa1de3941297_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#118;&#43;&#53;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#114;&#101;&#32;&#97;&#114;&#101;&#32;&#110;&#111;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#116;&#111;&#32;&#99;&#111;&#109;&#98;&#105;&#110;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#110;&#32;&#116;&#104;&#105;&#115;&#32;&#99;&#97;&#115;&#101;&#44;&#32;&#116;&#104;&#101;&#32;&#112;&#111;&#108;&#121;&#110;&#111;&#109;&#105;&#97;&#108;&#32;&#105;&#115;&#32;&#117;&#110;&#99;&#104;&#97;&#110;&#103;&#101;&#100;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#118;&#43;&#53;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"505\" style=\"vertical-align: -25px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836571078\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836387371\">\n<div data-type=\"problem\" id=\"fs-id1167836560357\">\n<p id=\"fs-id1167836287957\">Add: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-dc97bfff8019571d40b8de4eeba7fad9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"120\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-537805e12e84cd5debc0dbda84c05197_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"148\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836528200\">\n<p id=\"fs-id1167836492113\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-51ffe6954e65df84afe3c3c556e36021_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#123;&#122;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cf855d10c8d87cb5e321dc5f92f9a93c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"144\" style=\"vertical-align: -2px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836756832\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167824584640\">\n<div data-type=\"problem\" id=\"fs-id1167824584769\">\n<p id=\"fs-id1167829597034\">Add: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-91847e29b443c5afa0af220912deea4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#123;&#109;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"126\" style=\"vertical-align: -2px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8c32c921502d18509e896bac27cf569d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#112;&#45;&#53;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167824737606\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a6a1d0abda27c48c12d230db7a3aafd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"85\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5c8c322ed08565ee1d0ca11cc0ebbd9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#112;&#45;&#53;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<p>We can think of adding and subtracting polynomials as just adding and subtracting a series of monomials. Look for the like terms\u2014those with the same variables and the same exponent. The Commutative Property allows us to rearrange the terms to put like terms together.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836289213\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167833139745\">\n<div data-type=\"problem\" id=\"fs-id1167833056480\">\n<p id=\"fs-id1167833056483\">Find the sum:<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-46d1ca8d9469f529a4dede5b0645af42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#121;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#121;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"252\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829614243\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-571aacc918c2eaeb79c8a0352eb1a7c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#100;&#101;&#110;&#116;&#105;&#102;&#121;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#55;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#125;&#123;&#50;&#121;&#125;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#125;&#123;&#56;&#121;&#125;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#101;&#119;&#114;&#105;&#116;&#101;&#32;&#119;&#105;&#116;&#104;&#111;&#117;&#116;&#32;&#116;&#104;&#101;&#32;&#112;&#97;&#114;&#101;&#110;&#116;&#104;&#101;&#115;&#101;&#115;&#44;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#101;&#97;&#114;&#114;&#97;&#110;&#103;&#105;&#110;&#103;&#32;&#116;&#111;&#32;&#103;&#101;&#116;&#32;&#116;&#104;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#116;&#111;&#103;&#101;&#116;&#104;&#101;&#114;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#125;&#123;&#55;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#125;&#123;&#50;&#121;&#45;&#56;&#121;&#125;&#43;&#57;&#45;&#55;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#109;&#98;&#105;&#110;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#49;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#48;&#121;&#43;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"90\" style=\"vertical-align: -164px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836539576\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836447632\">\n<div data-type=\"problem\" id=\"fs-id1167836309244\">\n<p id=\"fs-id1167836309246\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-96e73d9c6066cf630827853f6f17d0ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"246\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829586793\">\n<p id=\"fs-id1167829586795\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e1cef4ea7d9f573e5844670f8133960a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#49;&#120;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"107\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167824736146\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167833385425\">\n<div data-type=\"problem\" id=\"fs-id1167833385427\">\n<p id=\"fs-id1167833071635\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9168a19d4463d179cd4f43bcba562582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#121;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"261\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167825703487\">\n<p id=\"fs-id1167825703489\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-64230c1cf11db0b4360928ebb0a5030a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#52;&#121;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1171790896470\">Be careful with the signs as you distribute while subtracting the polynomials in the next example.<\/p>\n<div data-type=\"example\" id=\"fs-id1167829749490\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167829749492\">\n<div data-type=\"problem\" id=\"fs-id1167836522315\">\n<p id=\"fs-id1167836522317\">Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-00d8fd1bd6422f70c62fb8cbd70828dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#119;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"223\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836731036\">\n<p id=\"fs-id1167836756613\">\n<pre class=\"ql-errors\">*** QuickLaTeX cannot compile formula:\n&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#119;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#105;&#115;&#116;&#114;&#105;&#98;&#117;&#116;&#101;&#32;&#97;&#110;&#100;&#32;&#105;&#100;&#101;&#110;&#116;&#105;&#102;&#121;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#125;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#125;&#123;&#55;&#119;&#125;&#43;&#53;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#50;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#125;&#125;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#101;&#97;&#114;&#114;&#97;&#110;&#103;&#101;&#32;&#116;&#104;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#95;&#125;&#123;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#125;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#125;&#123;&#55;&#119;&#125;&#43;&#53;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#109;&#98;&#105;&#110;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#55;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#119;&#43;&#57;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\n\n*** Error message:\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#123;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#46;&#46;&#46;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#123;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#46;&#46;&#46;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#123;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#46;&#46;&#46;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#123;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#46;&#46;&#46;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#125;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#46;&#46;&#46;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#125;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#46;&#46;&#46;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#125;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#46;&#46;&#46;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#125;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#46;&#46;&#46;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#123;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#46;&#46;&#46;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\r\n&#77;&#105;&#115;&#115;&#105;&#110;&#103;&#32;&#123;&#32;&#105;&#110;&#115;&#101;&#114;&#116;&#101;&#100;&#46;\r\n&#108;&#101;&#97;&#100;&#105;&#110;&#103;&#32;&#116;&#101;&#120;&#116;&#58;&#32;&#46;&#46;&#46;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#95;&#95;&#95;&#95;&#125;&#123;&#57;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#125;&#125;\r\n\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833339032\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167833339035\">\n<div data-type=\"problem\" id=\"fs-id1167836620467\">\n<p id=\"fs-id1167836620470\">Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-11bb525716503b1ce2e02256ba8b9ce5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#45;&#49;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"232\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836543282\">\n<p id=\"fs-id1167836543285\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-90a5d1a4157ac8ee7b9323ff8f23431f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829585676\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829585679\">\n<div data-type=\"problem\" id=\"fs-id1167836447528\">\n<p id=\"fs-id1167836447530\">Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-30e82cda9b61c020bbcdc787225e9bb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#98;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#98;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"245\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829832094\">\n<p id=\"fs-id1167836533016\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c48b0ada4fd2c5c995ceb5eb10f6c39e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"55\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1171790290366\">To subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a521efcd0a946cd643aebe98b5b41a3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"12\" style=\"vertical-align: -4px;\" \/> we write it as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-984fd759eee5d6fed25078dce8442ab2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#45;&#97;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/> placing the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> first.<\/p>\n<div data-type=\"example\" id=\"fs-id1167833049950\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167833049952\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167833339601\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-45e212a345126619c6d2364153be2055_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#48;&#112;&#113;&#45;&#50;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"132\" style=\"vertical-align: -7px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4c16005a925f958fd686c24326a30dc6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"76\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836706818\">\n<p id=\"fs-id1167833057701\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ba8848fe3cfa9fd7919dae3c41464a7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#48;&#112;&#113;&#45;&#50;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#105;&#115;&#116;&#114;&#105;&#98;&#117;&#116;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#48;&#112;&#113;&#43;&#50;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#101;&#97;&#114;&#114;&#97;&#110;&#103;&#101;&#32;&#116;&#104;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#44;&#32;&#116;&#111;&#32;&#112;&#117;&#116;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#116;&#111;&#103;&#101;&#116;&#104;&#101;&#114;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#48;&#112;&#113;&#43;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#109;&#98;&#105;&#110;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#49;&#48;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"650\" style=\"vertical-align: -37px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167824733970\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836416627\">\n<div data-type=\"problem\" id=\"fs-id1167836416629\">\n<p id=\"fs-id1167836416631\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-636165ebe0ab0cad40490e4dbd4c97e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#97;&#98;&#45;&#54;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"123\" style=\"vertical-align: -7px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c085e737f5d66a0b8a906eaac11e0459_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836557087\">\n<p id=\"fs-id1167836557089\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-224eb2e37617e5f9cffea2938f00344b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#97;&#98;&#43;&#55;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"84\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829853708\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829853711\">\n<div data-type=\"problem\" id=\"fs-id1167836493326\">\n<p id=\"fs-id1167836493328\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-73dec27c900d3c35289af620d2702353_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#109;&#110;&#45;&#51;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"141\" style=\"vertical-align: -7px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2e76b0dd796dd942f8a3902a8a844962_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"84\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836665216\">\n<p id=\"fs-id1167836665218\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a59ac81b6a04979a505c01075b35690b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#109;&#110;&#43;&#52;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"84\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"example\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167833412566\">\n<p id=\"fs-id1167836730201\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a4f6f2772d0646f7a5e61411d1712813_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#117;&#118;&#43;&#53;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#117;&#118;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"251\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836558032\">\n<p id=\"fs-id1167836558034\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-703a3c711a1910dc6c6a36f8380daf7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#117;&#118;&#43;&#53;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#117;&#118;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#105;&#115;&#116;&#114;&#105;&#98;&#117;&#116;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#117;&#118;&#43;&#53;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#117;&#118;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#101;&#97;&#114;&#114;&#97;&#110;&#103;&#101;&#32;&#116;&#104;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#116;&#111;&#32;&#112;&#117;&#116;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#116;&#111;&#103;&#101;&#116;&#104;&#101;&#114;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#117;&#118;&#43;&#50;&#117;&#118;&#43;&#53;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#109;&#98;&#105;&#110;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#117;&#118;&#43;&#53;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"216\" width=\"663\" style=\"vertical-align: -101px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836552919\">\n<div data-type=\"problem\" id=\"fs-id1167836552921\">\n<p id=\"fs-id1167833382187\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ba0a7887d75bc4a83ac552e552490cea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#120;&#121;&#43;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"251\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836424170\">\n<p id=\"fs-id1167836602764\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-124eb927f4908a7d3acf2a2b4135001c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#121;&#43;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836689192\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836689195\">\n<div data-type=\"problem\" id=\"fs-id1167836689197\">\n<p id=\"fs-id1167836624073\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e1affab64e6e3b46dedccc79cf21b40a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#121;&#45;&#50;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"260\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833036790\">\n<p id=\"fs-id1167836756749\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-84efa5ef8435d8e1e9154e046c4060f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#120;&#121;&#45;&#50;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1171792799230\">When we add and subtract more than two polynomials, the process is the same.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836423838\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836423840\">\n<div data-type=\"problem\" id=\"fs-id1167836507496\">\n<p id=\"fs-id1167836507498\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7b44b8eaf0f0bc5152a9c6b2195cdb95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#43;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"293\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836560662\">\n<p id=\"fs-id1167836560664\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7df08151a687fa54c4597bf56420cc63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#43;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#68;&#105;&#115;&#116;&#114;&#105;&#98;&#117;&#116;&#101;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#45;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#43;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#43;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#101;&#119;&#114;&#105;&#116;&#101;&#32;&#119;&#105;&#116;&#104;&#111;&#117;&#116;&#32;&#116;&#104;&#101;&#32;&#112;&#97;&#114;&#101;&#110;&#116;&#104;&#101;&#115;&#101;&#115;&#44;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#101;&#97;&#114;&#114;&#97;&#110;&#103;&#105;&#110;&#103;&#32;&#116;&#111;&#32;&#103;&#101;&#116;&#32;&#116;&#104;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#32;&#116;&#111;&#103;&#101;&#116;&#104;&#101;&#114;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#43;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#45;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#109;&#98;&#105;&#110;&#101;&#32;&#108;&#105;&#107;&#101;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"237\" width=\"662\" style=\"vertical-align: -111px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167829594555\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167829594558\">\n<div data-type=\"problem\" id=\"fs-id1167836493517\">\n<p id=\"fs-id1167836493519\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c7ec8bc0487d5b54f86efa39379da70d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#43;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"305\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832961272\">\n<p id=\"fs-id1167832961274\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f729489b70d102f485d5691dff0e4a1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836293746\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836293749\">\n<div data-type=\"problem\" id=\"fs-id1167836293752\">\n<p id=\"fs-id1167829930564\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5a4b2bcbcefcdad70d51eb4a3d1c9b4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#113;&#43;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"296\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833030913\">\n<p id=\"fs-id1167833030915\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d649a3c9eeb69d35d8252b878cbd90d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#45;&#51;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#113;&#43;&#123;&#113;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167836624599\">\n<h3 data-type=\"title\">Evaluate a Polynomial Function for a Given Value<\/h3>\n<p id=\"fs-id1167833381572\">A <span data-type=\"term\">polynomial function<\/span> is a function defined by a polynomial. For example, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7e31b988934069c51bdc795e191df093_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"150\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a75efe7e6979bc3115f409e747d1a578_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"109\" style=\"vertical-align: -4px;\" \/> are polynomial functions, because <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-796dbf4877c44d45b95e2f7845612068_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-27650edef34d7a09966de7ca79363ba4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"50\" style=\"vertical-align: -1px;\" \/> are polynomials.<\/p>\n<div data-type=\"note\" id=\"fs-id1167836511381\">\n<div data-type=\"title\">Polynomial Function<\/div>\n<p id=\"fs-id1167836596338\">A <strong data-effect=\"bold\">polynomial function<\/strong> is a function whose range values are defined by a polynomial.<\/p>\n<\/div>\n<p id=\"fs-id1167836294033\">In <a href=\"\/contents\/4d690921-1182-4ad3-86e0-7f849efbd233\" class=\"target-chapter\">Graphs and Functions<\/a>, where we first introduced functions, we learned that evaluating a function means to find the value of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-984a3dd11ed3c9a1f42d61a2defb75e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"36\" style=\"vertical-align: -4px;\" \/> for a given value of <em data-effect=\"italics\">x<\/em>. To evaluate a polynomial function, we will substitute the given value for the variable and then simplify using the order of operations.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836619473\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836619475\">\n<div data-type=\"problem\" id=\"fs-id1167829694499\">\n<p id=\"fs-id1167829694501\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7784892aae58f0ad80635121274a6069_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"159\" style=\"vertical-align: -4px;\" \/> find: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c5ca7959d454ac362604a7c61a837ac7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-dca5d7bc047aaa23a5ac85a2c257c5f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"49\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836477533\">\n<p id=\"fs-id1167836477535\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<table id=\"fs-id1167829741803\" class=\"unnumbered unstyled\" summary=\"The image shows a series of equations with instructions. The first equation is the function equation f of x equals 5 x squared minus 8 x plus 4. To find f of 4, substitute 4 for x. The second equation is f of 4 equals 5 times 4 squared minus 8 times 4 plus 4. The 4\u2019s replacing x are emphasized. The remaining equations show how to simplify the right side of the equation using the order of operations. The third equation is f of 4 equals 5 times 16 minus 8 times 4 plus 4. The fourth equation is f of 4 equals 80 minus 32 plus 4. The last equation is f of 4 equals 52.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836391910\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_004b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_004a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span>\u2003\u2003<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829597649\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_004c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify the exponents.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833061150\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_004d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Multiply.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836635636\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_004e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833056901\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_004f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167836557376\"><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<table id=\"fs-id1167836557383\" class=\"unnumbered unstyled\" summary=\"The image shows a series of equations with instructions. The first equation is the function equation f of x equals 5 x squared minus 8 x plus 4. To find f of negative 2, substitute negative 2 for x. The second equation is f of negative 2 equals 5 times negative 2 squared minus 8 times negative 2 plus 4. The negative 2\u2019s replacing x are emphasized. The remaining equations show how to simplify the right side of the equation using the order of operations. The third equation is f of negative 2 equals 5 times 4 minus 8 times negative 2 plus 4. The fourth equation is f of negative 2 equals 20 plus 16 plus 4. The last equation is f of negative 2 equals 40.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836520680\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_005b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836515645\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_005a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span>\u2003<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167832999661\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_005c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify the exponents.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836362540\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_005d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Multiply.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836738242\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_005e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836534829\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_005f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167836700907\"><span class=\"token\">\u24d2<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<table id=\"fs-id1167836606920\" class=\"unnumbered unstyled\" summary=\"The image shows a series of equations with instructions. The first equation is the function equation f of x equals 5 x squared minus 8 x plus 4. To find f of 0, substitute 0 for x. The second equation is f of 0 equals 5 times 0 squared minus 8 times 0 plus 4. The 0\u2019s replacing x are emphasized. The remaining equations show how to simplify the right side of the equation using the order of operations. The third equation is f of 0 equals 5 times 0 minus 8 times 0 plus 4. The fourth equation is f of 0 equals 0 plus 0 plus 4. The last equation is f of 0 equals 4.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829690356\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_006b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833059281a\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_006a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span>\u2003\u2003<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833059281\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_006c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify the exponents.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836492694\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_006d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Multiply.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833339022\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_006e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Simplify.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167832999463\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_006f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836532480\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836532484\">\n<div data-type=\"problem\" id=\"fs-id1167836532486\">\n<p id=\"fs-id1167836520974\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f429a7384bff41366cf98f2a65bb4a70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#120;&#45;&#49;&#53;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"172\" style=\"vertical-align: -4px;\" \/> find <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b7454c1320ac593411a470ad12380405_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-08a61ef571ebff4c4d0c33bf7601a8f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"49\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-db4f958b4c4deacd90047ad0c954283a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836560811\">\n<p id=\"fs-id1167836560813\"><span class=\"token\">\u24d0<\/span> 18 <span class=\"token\">\u24d1<\/span> 50 <span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0329d19b932005c996d83dbb9e09ffed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836377469\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836377474\">\n<div data-type=\"problem\" id=\"fs-id1167836377476\">\n<p id=\"fs-id1167836515904\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2b04aca54417c9ba729e841eca7cb2ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#45;&#52;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -4px;\" \/> find <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b9c162672a0d27d74bc1198fa177afdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"48\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c180bd3dc0c2ee1eaf25f823f5a72c32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"48\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-613732596c873f6601a1909111a49aba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836507429\">\n<p id=\"fs-id1167836507431\"><span class=\"token\">\u24d0<\/span> 20 <span class=\"token\">\u24d1<\/span> 2 <span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-00b9cce9021441b203ec0271d72e6ba2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829580335\">The polynomial functions similar to the one in the next example are used in many fields to determine the height of an object at some time after it is projected into the air. The polynomial in the next function is used specifically for dropping something from 250 ft.<\/p>\n<div data-type=\"example\" id=\"fs-id1167836494121\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836494123\">\n<div data-type=\"problem\" id=\"fs-id1167836494125\">\n<p id=\"fs-id1167836494127\">The polynomial function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5641618203c7ab02b04d7fa1616b2510_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -4px;\" \/> gives the height of a ball <em data-effect=\"italics\">t<\/em> seconds after it is dropped from a 250-foot tall building. Find the height after <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-eec54adef7198c4decb9169a2b472009_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"38\" style=\"vertical-align: 0px;\" \/> seconds.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836596028\">\n<p id=\"fs-id1167836596030\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-afa703d6b1f750323ee14119c6a7466d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#53;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#111;&#32;&#102;&#105;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#98;&#115;&#116;&#105;&#116;&#117;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#116;&#61;&#50;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#54;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#53;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#54;&middot;&#52;&#43;&#50;&#53;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#54;&#52;&#43;&#50;&#53;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#105;&#109;&#112;&#108;&#105;&#102;&#121;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#56;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#102;&#116;&#101;&#114;&#32;&#50;&#32;&#115;&#101;&#99;&#111;&#110;&#100;&#115;&#32;&#116;&#104;&#101;&#32;&#104;&#101;&#105;&#103;&#104;&#116;&#32;&#111;&#102;&#32;&#116;&#104;&#101;&#32;&#98;&#97;&#108;&#108;&#32;&#105;&#115;&#32;&#49;&#56;&#54;&#32;&#102;&#101;&#101;&#116;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"196\" width=\"659\" style=\"vertical-align: -92px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836628296\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167836606842\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167836606847\">The polynomial function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-33e8d87edc1a7080b49e4b3ea3be1c5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -4px;\" \/> gives the height of a stone <em data-effect=\"italics\">t<\/em> seconds after it is dropped from a 150-foot tall cliff. Find the height after <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b7b41acc5cb99fb07aaa07b445eb2483_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\" \/> seconds (the initial height of the object).<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836730595\">\n<p id=\"fs-id1167836706618\">The height is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-74a92b6c533b233c6f544c969f0e81fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"26\" style=\"vertical-align: -1px;\" \/> feet.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167833082429\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167833082432\">\n<div data-type=\"problem\" id=\"fs-id1167836546926\">\n<p id=\"fs-id1167836546928\">The polynomial function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-717d79a2460888e6a98e739eb8ee5de5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"150\" style=\"vertical-align: -4px;\" \/> gives the height of a ball <em data-effect=\"italics\">t<\/em> seconds after it is dropped from a 175-foot tall bridge. Find the height after <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0807de1d4e00db15c6d9ac7e73ae67b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\" \/> seconds.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833051269\">\n<p id=\"fs-id1167833051271\">The height is 31 feet.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167829719032\">\n<h3 data-type=\"title\">Add and Subtract Polynomial Functions<\/h3>\n<p id=\"fs-id1167833224796\">Just as polynomials can be added and subtracted, polynomial functions can also be added and subtracted.<\/p>\n<div data-type=\"note\" id=\"fs-id1167833224799\">\n<div data-type=\"title\">Addition and Subtraction of Polynomial Functions<\/div>\n<p id=\"fs-id1167833224804\">For functions <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-984a3dd11ed3c9a1f42d61a2defb75e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"36\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-344231958daaa52c1755b0b6892d4016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"equation\" id=\"fs-id1167836508945\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2478a8a4bb9e3114738edd88fa8fd0aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"199\" style=\"vertical-align: -15px;\" \/><\/div>\n<\/div>\n<div data-type=\"example\" id=\"fs-id1167836717235\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167836717237\">\n<div data-type=\"problem\" id=\"fs-id1167836717240\">\n<p id=\"fs-id1167836717242\">For functions <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-df50ae4ff7da94eb47d800583d4d4750_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"159\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-706c5fad0783000d3f1a5e34983ea8f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#120;&#45;&#51;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -4px;\" \/> find:<\/p>\n<p id=\"fs-id1167829872138\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b1f7743bc12c43eb246486a8c39b5fbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0d4c24bc5884d5327153d175581a0629_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f66316491cb564a03a7edaa9e6d0419a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-09f1c1ff3bbae7ca431804562be5fc87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832982204\">\n<p id=\"fs-id1167832982206\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<table id=\"fs-id1167836391919\" class=\"unnumbered unstyled\" summary=\"The figure shows a series of equations in function notation. The first equation is the formula f plus g of x equals f of x plus g of x. Substituting f of x equals 3 x squared minus 5 x plus 7 and g of x equals x squared minus 4 x minus 3 into the formula results in the equation f plus g of x equals the quantity 3 x squared minus 5 x plus 7 in parentheses plus the quantity x squared minus 4 x minus 3 in parentheses. Rewriting without parentheses is the equation f plus g of x equals 3 x squared minus 5 x plus 7 plus x squared minus 4 x minus 3. Putting like terms together results in the equation f plus g of x equals 3 x squared plus x squared minus 5 x minus 4 x plus 7 minus 3. Combining like terms results in the fully simplified function equation f plus g of x equals 4 x squared minus 9 x plus 4.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836326099\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_007b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829861746\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_007a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836624089\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_007c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Rewrite without the parentheses.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829695341\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_007d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Put like terms together.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829627739\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_007e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Combine like terms.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833407424\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_007f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167836730613\"><span class=\"token\">\u24d1<\/span> In part (a) we found <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b1f7743bc12c43eb246486a8c39b5fbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/> and now are asked to find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e92a7d5ccf73a31cd604b1e51ab7e279_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8ebe6c670591f0c1110c3ff5aeb93d18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#120;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#111;&#32;&#102;&#105;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#98;&#115;&#116;&#105;&#116;&#117;&#116;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#120;&#61;&#51;&#46;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&middot;&#51;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&middot;&#57;&#45;&#57;&middot;&#51;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#54;&#45;&#50;&#55;&#43;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"219\" width=\"548\" style=\"vertical-align: -104px;\" \/><\/p>\n<p id=\"fs-id1167836660081\">Notice that we could have found <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0d4c24bc5884d5327153d175581a0629_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/> by first finding the values of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b7454c1320ac593411a470ad12380405_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e2adbcd4624c8f3e37ee45ba3f66530b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -4px;\" \/> separately and then adding the results.<\/p>\n<table id=\"fs-id1167829748066\" class=\"unnumbered unstyled\" summary=\"The figure shows a series of calculations to verify the last result. The first calculation is labeled Find f of 3. The first equation is the function equation f of x equals 3 x squared minus 5 x plus 7. The second equation is f of 3 equals 3 times 3 squared minus 5 times 3 plus 7, where the 3\u2019s are all emphasized. The third equation is f of 3 equals 19. The second calculation is labeled Find g of 3. The first equation is the function equation g of x equals x squared minus 4 x minus 3. The second equation is g of 3 equals 3 squared minus 4 times 3 minus 3. The 3\u2019s that replaced the x\u2019s are emphasized. The next equation is g of 3 equals negative 6. The last calculation is labeled Find f plus g of 3. The first equation is the formula f plus g of x equals f of x plus g of x. The second equation is f plus g of 3 equals f of 3 plus g of 3. Substituting f of 3 equals 19 and g of 3 equals negative 6 we get the equation f plus g of 3 equals 19 minus 6. The last equation is f plus g of 3 equals 13.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e2d15f1465e8ad2b3d524cbce299db86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"43\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829743187\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829745681\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836614824\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-46e63ebcaf7174459b89e4ae8e8b393b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833338871\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833024470\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167832945745\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008g_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e92a7d5ccf73a31cd604b1e51ab7e279_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"87\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829579194\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008h_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833066755\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008i_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836391940\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f124c07c12a79524bccd7af3772b6a07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836536972\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008j_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836601705\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_008k_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167833378545\"><span class=\"token\">\u24d2<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<table id=\"fs-id1167832982035\" class=\"unnumbered unstyled\" summary=\"The figure shows a series of equations in function notation. The first equation is the formula f minus g of x equals f of x minus g of x. Substituting f of x equals 3 x squared minus 5 x plus 7 and g of x equals x squared minus 4 x minus 3 into the formula results in the equation f minus g of x equals the quantity 3 x squared minus 5 x plus 7 in parentheses minus the quantity x squared minus 4 x minus 3 in parentheses. Rewriting without parentheses is the equation f minus g of x equals 3 x squared minus 5 x plus 7 minus x squared plus 4 x plus 3. Putting like terms together results in the equation f minus g of x equals 3 x squared minus x squared minus 5 x plus 4 x plus 7 plus 3. Combining like terms results in the fully simplified function equation f minus g of x equals 2 x squared minus x plus 10.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167836625927\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_009b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829593569\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_009a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829717196\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_009c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Rewrite without the parentheses.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833338979\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_009d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Put like terms together.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829692985\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_009e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Combine like terms.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167833227243\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_009f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1167833060375\"><span class=\"token\">\u24d3<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<table id=\"fs-id1167832937173\" class=\"unnumbered unstyled\" summary=\"The figure shows a series of equations in function notation. The first equation is the equation f minus g of x equals 2 x squared minus x plus 10. To find f minus g of negative 2 substitute x equals negative 2. The second equation is f minus g of negative 2 equals 2 times negative 2 squared minus negative 2 plus 10. The next equation is f minus g of negative 2 equals 2 times 4 minus negative 2 plus 10. The next equation is f minus g of negative 2 equals 20.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167829739277\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_010_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167824734625\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167824734629\">\n<div data-type=\"problem\" id=\"fs-id1167824734631\">\n<p id=\"fs-id1167824734633\">For functions <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cb69c653151f7407b7ac5703a04188fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"159\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cd7ca9eff67acf3a9cad8b1bbff34a7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#120;&#45;&#54;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -4px;\" \/> find: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b1f7743bc12c43eb246486a8c39b5fbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0d4c24bc5884d5327153d175581a0629_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f66316491cb564a03a7edaa9e6d0419a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d3<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-09f1c1ff3bbae7ca431804562be5fc87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829811159\">\n<p id=\"fs-id1167829811161\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d5d729d7d4f68a9036c653b418ba8102_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"203\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-80bcb9b2d54cd37224713bb97b78c3e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f9d2e805a871ca14bcea63e1fe40d170_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#120;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3f0818ab07dca5dab4c3214b0cc19ae7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"135\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836619815\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167830076287\">\n<div data-type=\"problem\" id=\"fs-id1167830076289\">\n<p id=\"fs-id1167830076291\">For functions <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1fd0c61aa41ea31839a04166a1b57b3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-766ac9e817ec982349a6d82ab8527433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#43;&#56;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -4px;\" \/> find <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b1f7743bc12c43eb246486a8c39b5fbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0d4c24bc5884d5327153d175581a0629_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"79\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f66316491cb564a03a7edaa9e6d0419a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d3<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-09f1c1ff3bbae7ca431804562be5fc87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"100\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167829614420\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6d20cb1fa39d3bd0725d821ed4492e8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f2fe5c408c31f7d4b7c5916c3192669f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ed928daf989d3247c9a9ed3a50cc244a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#120;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"203\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-30d0d736ccfa4347739c28a0a12653d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"134\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167836594852\" class=\"media-2\">\n<p id=\"fs-id1167836594856\">Access this online resource for additional instruction and practice with adding and subtracting polynomials.<\/p>\n<ul id=\"fs-id1167836594861\" data-bullet-style=\"bullet\">\n<li><a href=\"https:\/\/openstax.org\/l\/37AddSubtrPoly\">Adding and Subtracting Polynomials<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167824584895\">\n<h3 data-type=\"title\">Key Concepts<\/h3>\n<ul id=\"fs-id1167829828750\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Monomial<\/strong>\n<ul id=\"fs-id1167836409466\" data-bullet-style=\"bullet\">\n<li>A <strong data-effect=\"bold\">monomial<\/strong> is an algebraic expression with one term.<\/li>\n<li>A monomial in one variable is a term of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f8fe74b3bd004d025e1a2dce9b428a1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#123;&#120;&#125;&#94;&#123;&#109;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"36\" style=\"vertical-align: -4px;\" \/> where <em data-effect=\"italics\">a<\/em> is a constant and <em data-effect=\"italics\">m<\/em> is a whole number.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Polynomials<\/strong>\n<ul id=\"fs-id1167836625101\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Polynomial<\/strong>\u2014A monomial, or two or more algebraic terms combined by addition or subtraction is a polynomial.<\/li>\n<li><strong data-effect=\"bold\">monomial<\/strong> \u2014A polynomial with exactly one term is called a monomial.<\/li>\n<li><strong data-effect=\"bold\">binomial<\/strong> \u2014 A polynomial with exactly two terms is called a binomial.<\/li>\n<li><strong data-effect=\"bold\">trinomial<\/strong> \u2014A polynomial with exactly three terms is called a trinomial.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Degree of a Polynomial<\/strong>\n<ul id=\"fs-id1167836756827\" data-bullet-style=\"bullet\">\n<li>The <strong data-effect=\"bold\">degree of a term<\/strong> is the sum of the exponents of its variables.<\/li>\n<li>The <strong data-effect=\"bold\">degree of a constant<\/strong> is 0.<\/li>\n<li>The <strong data-effect=\"bold\">degree of a polynomial<\/strong> is the highest degree of all its terms.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167829713312\">\n<div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1167829713317\">\n<h4 data-type=\"title\">Practice Makes Perfect<\/h4>\n<p id=\"fs-id1167829713324\"><strong data-effect=\"bold\">Determine the Type of Polynomials<\/strong><\/p>\n<p id=\"fs-id1167836408265\">In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial.<\/p>\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167836408272\">\n<p id=\"fs-id1167836408274\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d91a7a0f11d3047304318bf12767959c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#55;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#45;&#49;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#43;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"148\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0ecf5c88f925435635dc33fab094a736_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#99;&#125;&#94;&#123;&#51;&#125;&#43;&#49;&#49;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#45;&#99;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"139\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0ef864a547a5819551f824c98ffc3300_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#57;&#125;&#97;&#98;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"66\" style=\"vertical-align: -6px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span> 4<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5697f38166ad534a04c15ca228e26939_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#112;&#113;&#43;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167829627905\">\n<p id=\"fs-id1167829627907\"><span class=\"token\">\u24d0<\/span> trinomial, 5 <span class=\"token\">\u24d1<\/span> polynomial, 3 <span class=\"token\">\u24d2<\/span> binomial, 1 <span class=\"token\">\u24d3<\/span> monomial, 1<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span> binomial, 1<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836512992\">\n<div data-type=\"problem\" id=\"fs-id1167836512994\">\n<p id=\"fs-id1167836512996\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7d384e8452ec799493816529fe1636d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-509eb751471364e6cc269a7141441d4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#51;&#123;&#99;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"46\" style=\"vertical-align: -1px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-442a36d187c24bfa3f95901a9f154e93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#97;&#98;&#45;&#55;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"110\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-999b5e96d6187121c1add89dff67460b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#121;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span> 19<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832937207\">\n<div data-type=\"problem\" id=\"fs-id1167832937209\">\n<p id=\"fs-id1167832937211\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a7d0ce1063abe81b96c76aa64f09fbb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#121;&#45;&#53;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a4d21f724711003ec7d646b21700c68b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#121;&#122;&#45;&#54;&#123;&#122;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9af5a4500fe4df222ef6b619ff98c7db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#121;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e53f4fdfeac632aa988469adbdb68a64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;&#97;&#123;&#98;&#125;&#94;&#123;&#52;&#125;&#45;&#50;&#52;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"153\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bb9e52ddecc045b16dbf509b1c89f11b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836596290\">\n<p id=\"fs-id1167836596292\"><span class=\"token\">\u24d0<\/span> binomial <span class=\"token\">\u24d1<\/span> trinomial<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span> polynomial <span class=\"token\">\u24d3<\/span> trinomial<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span> monomial <\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833009337\">\n<div data-type=\"problem\" id=\"fs-id1167833009340\">\n<p id=\"fs-id1167833009342\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-20708a39bd11237305557138f800d169_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-60817a5dc6e8a10974c6ee7ef7746d72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7d0cc63673af92bc002bbe7c5f3d13cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#121;&#43;&#52;&#120;&#45;&#50;&#121;&#43;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"195\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ade4a8c055fcc4b97e10e79a21babaa7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#55;&#123;&#122;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0ecf5c88f925435635dc33fab094a736_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#99;&#125;&#94;&#123;&#51;&#125;&#43;&#49;&#49;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#45;&#99;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"139\" style=\"vertical-align: -2px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836321250\">\n<div data-type=\"problem\" id=\"fs-id1167836321253\">\n<p id=\"fs-id1167836321255\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9bb3abd405cef166230070da373b9104_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#97;&#98;&#45;&#55;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"128\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1a5299bef0660a08c7a7408d37a61124_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1f967377cc0fea33b3cf57b2a701b2f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"49\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9af5a4500fe4df222ef6b619ff98c7db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#121;&#45;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d15aa1d60ab00024197b84d5e3e3d75e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167829684015\">\n<p id=\"fs-id1167829684017\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-36f39a5798d2720edfd78a9324897305_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-15f5671b3362f2067078fb12d95cd4da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f95b8779fb09b1edff84210cb701b98a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"15\" style=\"vertical-align: -1px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-15f5671b3362f2067078fb12d95cd4da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-66b0e0316f97b4df46a4ab4d9b940ce4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#48;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829741538\">\n<div data-type=\"problem\" id=\"fs-id1167829741540\">\n<p id=\"fs-id1167829741542\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-994883d2651845e99da2409d5f756bd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#48;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#121;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"153\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-162f2e45404ad07461289693b9962bcb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"55\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bbab4b1949c6e7d698de46cc7eda5721_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#97;&#98;&#43;&#49;&#56;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"119\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4616df992e28be77b9910ab7fcdbba38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#48;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"164\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span> 17<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826131747\">\n<div data-type=\"problem\" id=\"fs-id1167826131749\">\n<p id=\"fs-id1167826131751\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-285e84956c87f13004a66e3948211574_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#115;&#45;&#50;&#57;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"71\" style=\"vertical-align: -1px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3842251fb5e3ba785cf1fe99521ca652_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#122;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-53d9911d3355667c45a8e98ec5e22a5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#122;&#43;&#50;&#121;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#54;&#123;&#122;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"186\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fd88c8fcaba33d5667dc74cb96160d99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -1px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-470cb162cf92c55d139f4f69216225e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836730500\">\n<p id=\"fs-id1167836730502\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f95b8779fb09b1edff84210cb701b98a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#49;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"15\" style=\"vertical-align: -1px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-36f39a5798d2720edfd78a9324897305_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#50;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-15f5671b3362f2067078fb12d95cd4da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-15f5671b3362f2067078fb12d95cd4da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#51;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-66b0e0316f97b4df46a4ab4d9b940ce4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#48;&#125;&#94;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"16\" style=\"vertical-align: 0px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836598350\">\n<div data-type=\"problem\" id=\"fs-id1167836598352\">\n<p id=\"fs-id1167836598355\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b3aa0ca82239fd3d79eb3a1b485bcfae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#120;&#123;&#121;&#125;&#94;&#123;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"36\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span> 15<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7d0cc63673af92bc002bbe7c5f3d13cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#121;&#43;&#52;&#120;&#45;&#50;&#121;&#43;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"195\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-03b2ae1ce7e62b3c4990671236fdbfe8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#112;&#45;&#57;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"64\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d4<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3bd6b44fecde0b3983e0e81c9c3d6251_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#43;&#52;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#43;&#54;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#109;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"207\" style=\"vertical-align: -2px;\" \/><\/div>\n<\/div>\n<p id=\"fs-id1167829718398\"><strong data-effect=\"bold\">Add and Subtract Polynomials<\/strong><\/p>\n<p id=\"fs-id1167829718404\">In the following exercises, add or subtract the monomials.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829808015\">\n<div data-type=\"problem\" id=\"fs-id1167829808017\">\n<p id=\"fs-id1167829808019\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-15def4ed428fe4fa4bdd29d0f9088144_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#120;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#125;&#125;&#43;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"73\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8c6abb8e33d6644eee8a1f0f70d5c816_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#97;&#125;&#45;&#57;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"57\" style=\"vertical-align: -1px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836548593\">\n<p id=\"fs-id1167836548595\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0286ffd7884b40d995f2c3c624f3881e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#120;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"33\" style=\"vertical-align: -1px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-30c00a55b1d66272a46d02af77121844_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829627667\">\n<div data-type=\"problem\" id=\"fs-id1167829627669\">\n<p id=\"fs-id1167829627671\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cbc8d02e7cfe9a3a3a535e3c5c62aec1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#121;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#125;&#125;&#43;&#54;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3b238b2fa91d4ab6bed2f0225dac61b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#121;&#45;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"49\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826205230\">\n<div data-type=\"problem\" id=\"fs-id1167826205232\">\n<p id=\"fs-id1167826205234\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3974cd9e90afe314c8349a28b920ca68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#119;&#43;&#49;&#56;&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"96\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-14b52cf72d9d10381a546a979dc360b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"130\" style=\"vertical-align: -7px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836660180\">\n<p id=\"fs-id1167836660182\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7be5a31fdc2bce3a547dd5e09ef7a679_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#125;&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f808d10e673d4dd019b5dd411eace98b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836449588\">\n<div data-type=\"problem\" id=\"fs-id1167836449590\">\n<p id=\"fs-id1167836449592\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-59033055dac6f0748a6edaa4625c8c67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#109;&#43;&#57;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"83\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2d4c3f14417758bef50e2c359ad685c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#121;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#121;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"127\" style=\"vertical-align: -7px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167836621814\">\n<p id=\"fs-id1167836621816\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3f124ecdc7b21a53594c31314e56884b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#120;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#125;&#125;&#43;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#97;&#125;&#45;&#57;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"156\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829746749\">\n<p id=\"fs-id1167829746751\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8ed1a250f3d021ae0fcf2e8251712304_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#120;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#125;&#125;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"77\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833274103\">\n<div data-type=\"problem\" id=\"fs-id1167833274105\">\n<p id=\"fs-id1167833274108\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1e851fd5fc38f7cfc85b781c63fe3a26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#121;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#125;&#125;&#43;&#54;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#121;&#45;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833023422\">\n<div data-type=\"problem\" id=\"fs-id1167833023425\">\n<p id=\"fs-id1167833023427\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-911288a7b781b1455e471ccb09996b64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#119;&#43;&#49;&#56;&#119;&#43;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"248\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829906656\">\n<p id=\"fs-id1167829906658\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-745ff9f57ea63f90e1d4ca8fea34b19f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#119;&#43;&#49;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833021002\">\n<div data-type=\"problem\" id=\"fs-id1167833021004\">\n<p id=\"fs-id1167833021007\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0184a01cd5985399e6a62a48fa563446_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#109;&#43;&#57;&#109;&#43;&#49;&#53;&#121;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#121;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"233\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833021640\">\n<div data-type=\"problem\" id=\"fs-id1167833021642\">\n<p id=\"fs-id1167833021644\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-43f9dd4acc667b162b346ad70bda2339_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#98;&#45;&#49;&#55;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"77\" style=\"vertical-align: -1px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6677d72c28db6802d2605284e6c084e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#121;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#120;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#53;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"156\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167836789251\">\n<p id=\"fs-id1167836789253\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1640582004ab5d367f0827d925d31be9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#50;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b97e0c40d85f303a5081bb824c25ecac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"36\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836615678\">\n<div data-type=\"problem\" id=\"fs-id1167836615680\">\n<p id=\"fs-id1167836615683\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bd129f96e2a297a0061b583008f5b793_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#120;&#45;&#51;&#53;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"90\" style=\"vertical-align: -1px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a93f9356f4139f5af8f8796404029342_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#109;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#109;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;&#109;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"210\" style=\"vertical-align: -7px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836756594\">\n<div data-type=\"problem\" id=\"fs-id1167836756596\">\n<p id=\"fs-id1167836756598\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-703b395f213aa0fac9c8e10c988a3f99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#125;&#97;&#43;&#53;&#98;&#45;&#50;&#50;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"112\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c7a32039e8c88228ba67897f13b364b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#112;&#45;&#51;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167832925638\">\n<p id=\"fs-id1167832925640\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d5237a76bc9ccc35c98c44159dc38088_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#97;&#43;&#53;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"79\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c7a32039e8c88228ba67897f13b364b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#112;&#45;&#51;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836492076\">\n<div data-type=\"problem\" id=\"fs-id1167836492078\">\n<p id=\"fs-id1167836492080\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8b3dcb462c899d3ab66e11b1762199ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#52;&#120;&#125;&#45;&#51;&#121;&#45;&#49;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0a5b4b730fdd98090d58e48c05f61133_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#45;&#52;&#97;&#45;&#53;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"119\" style=\"vertical-align: -1px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832936422\">\n<div data-type=\"problem\" id=\"fs-id1167832936424\">\n<p id=\"fs-id1167832936426\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-dbe1fe9cb3a2c0e4db1d3b9fdb5cd8bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"110\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-241364c2a2e5ca36f254d8de958e74fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#45;&#51;&#120;&#43;&#55;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"125\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167833060532\">\n<p id=\"fs-id1167836552096\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-31ad64f942847e32638018ac9bd2b374_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"75\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-241364c2a2e5ca36f254d8de958e74fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#45;&#51;&#120;&#43;&#55;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"125\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836440002\">\n<div data-type=\"problem\" id=\"fs-id1167836440004\">\n<p id=\"fs-id1167836440006\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d8dc7dc94c0b0b509766f261f482c10b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#123;&#117;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"122\" style=\"vertical-align: -2px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3428874917688228e2ca78f2f7e485b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#97;&#125;&#43;&#56;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"64\" style=\"vertical-align: -2px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836596888\">\n<div data-type=\"problem\" id=\"fs-id1167836596890\">\n<p id=\"fs-id1167836596892\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-17aae8d8f94ea837257ac7a20244c005_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#45;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a334eca040775d069a889104b82efa92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#57;&#121;&#125;&#43;&#53;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"65\" style=\"vertical-align: -3px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167829930529\">\n<p id=\"fs-id1167829930531\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-17aae8d8f94ea837257ac7a20244c005_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#45;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-705de02a19ba2ee4ad1950e3b9dc3edf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#57;&#121;&#43;&#53;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836508704\">\n<div data-type=\"problem\" id=\"fs-id1167836508706\">\n<p id=\"fs-id1167836508708\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4b2bbe32cbf4d4262d60490b67ee8354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#125;&#97;&#43;&#53;&#98;&#45;&#50;&#50;&#97;&#43;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#112;&#45;&#51;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"245\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836406955\">\n<div data-type=\"problem\" id=\"fs-id1167836406957\">\n<p id=\"fs-id1167836406959\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5e176c3c03a5c4f66552147252b30526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#52;&#120;&#125;&#45;&#51;&#121;&#45;&#49;&#51;&#120;&#43;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#45;&#52;&#97;&#45;&#53;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"256\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836434024\">\n<p id=\"fs-id1167836434026\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-76681ca8603e8a775f711a857ee7f7ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#45;&#51;&#121;&#43;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#45;&#52;&#97;&#45;&#53;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"191\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836432063\">\n<div data-type=\"problem\" id=\"fs-id1167836423784\">\n<p id=\"fs-id1167836423787\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d323bcd937742d5488f0b06752c0926e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#45;&#51;&#120;&#43;&#55;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"257\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829747886\">\n<div data-type=\"problem\" id=\"fs-id1167829747888\">\n<p id=\"fs-id1167829747890\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8b133d98c7b11206ff4910349db5e6f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#97;&#125;&#43;&#56;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"213\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836409558\">\n<p id=\"fs-id1167836620844\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1786b2f38685d0270d37bdea83a3cd94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#43;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#97;&#125;&#43;&#56;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"156\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836292513\">\n<div data-type=\"problem\" id=\"fs-id1167836292515\">\n<p id=\"fs-id1167836737848\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c01768e1b06c999be2c2dec7b7a2a2b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#45;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#57;&#121;&#125;&#43;&#53;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"207\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833338729\">\n<div data-type=\"problem\" id=\"fs-id1167833338731\">\n<p id=\"fs-id1167833338733\">Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0d43fcd029f5c5ea62fca5d840d74134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#97;&#44;&#45;&#51;&#98;&#44;&#45;&#56;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832982010\">\n<p id=\"fs-id1167832982012\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-20317ce79cf7586b649176f304286b70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#97;&#125;&#45;&#51;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"56\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829712496\">\n<div data-type=\"problem\" id=\"fs-id1167829712498\">\n<p id=\"fs-id1167829712501\">Add:<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-27ee7b4218f5af4ce8f0dda8f384731a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#120;&#125;&#44;&#51;&#121;&#44;&#45;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"85\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833086506\">\n<div data-type=\"problem\" id=\"fs-id1167833086508\">\n<p id=\"fs-id1167836429801\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-31f2cfc59d6239205490278b9eda3c44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d4e6f082f5bf132a2c9380ef8d0dda6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"48\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167826025484\">\n<p id=\"fs-id1167826025486\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9a00f6d8de1dedfda274dcc67f503709_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#123;&#120;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826025500\">\n<div data-type=\"problem\" id=\"fs-id1167833197293\">\n<p id=\"fs-id1167833197295\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5b4523ae3ef38d56f4fbb90e0808c842_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#112;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"25\" style=\"vertical-align: -4px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d3eda7af3b21b05f2be20c94b5955080_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#123;&#112;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167824733268\">In the following exercises, add the polynomials.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167824733271\">\n<div data-type=\"problem\" id=\"fs-id1167824733273\">\n<p id=\"fs-id1167824733275\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e7a372ab3c0a06c27a2567ed6e0a0b1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#121;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#121;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"252\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836665099\">\n<p id=\"fs-id1167836665101\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-316a008455fcaaeda64c792a11759f6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#121;&#43;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829690282\">\n<div data-type=\"problem\" id=\"fs-id1167829690285\">\n<p id=\"fs-id1167829690287\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-35c59994878c78fccdc728f9b4b525a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#48;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"252\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833350072\">\n<div data-type=\"problem\" id=\"fs-id1167833350074\">\n<p id=\"fs-id1167833350076\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7f795b4521daa9611916ffd2c71818df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#120;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#49;&#120;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"260\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836732159\">\n<p id=\"fs-id1167836732161\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8a972d41d967d9d91be7f528234b2322_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#55;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"119\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829597471\">\n<div data-type=\"problem\" id=\"fs-id1167829597473\">\n<p id=\"fs-id1167829597475\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7271e76e2590b3c72efc66a8fc9071db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#121;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#121;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"248\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836356307\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167836456215\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8d35711d7b83615a962de64df7d23d8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"205\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833386390\">\n<p id=\"fs-id1167833386392\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-da9f177ddf56c34fcda258258cfb6d3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833128238\">\n<div data-type=\"problem\" id=\"fs-id1167833128240\">\n<p id=\"fs-id1167829788193\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c140a58f4c6f3ef3a8a5216e1696f7e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"205\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836561092\">\n<div data-type=\"problem\" id=\"fs-id1167836561095\">\n<p id=\"fs-id1167836561097\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8f426ac332b91e4032acb09963b7fff7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#97;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"194\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833385974\">\n<p id=\"fs-id1167833385976\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d9601d909a18e6024b1e4874868527a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#97;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"95\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829844347\">\n<div data-type=\"problem\" id=\"fs-id1167829844349\">\n<p id=\"fs-id1167829844351\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-249edff442c9af392f227870a122d51d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#112;&#45;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"211\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167833142618\">In the following exercises, subtract the polynomials.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167833142621\">\n<div data-type=\"problem\" id=\"fs-id1167833142624\">\n<p id=\"fs-id1167833142626\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d6d0acc472b085264e7dcc6b74c4e07d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#109;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#109;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"259\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829751095\">\n<p id=\"fs-id1167836508167\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1cacfe42298f3ff5c8f47953fe025761_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#109;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"109\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836398826\">\n<div data-type=\"problem\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ad3837e3b8744dd7c1451c16385cf726_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#98;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#98;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"227\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829834036\">\n<div data-type=\"problem\" id=\"fs-id1167829834038\">\n<p id=\"fs-id1167829834041\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3024c374b988968c4f146ac68c7b0247_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#97;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#97;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"225\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829621172\">\n<p id=\"fs-id1167829621175\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1921e9aa5e0e67e0e66ee0c9be0c7eb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#97;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"57\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829790417\">\n<div data-type=\"problem\" id=\"fs-id1167829790419\">\n<p id=\"fs-id1167829790421\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-54e706b035577a25a98172cbbc92f231_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#98;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#98;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"218\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836386461\">\n<div data-type=\"problem\" id=\"fs-id1167830096219\">\n<p id=\"fs-id1167830096222\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3023ac5fe9bc1299f658cf4fd4d9f1f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#53;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"169\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167829907673\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-98145ee3056d9a3ace1066f6759344d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#52;&#115;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"111\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836423564\">\n<div data-type=\"problem\" id=\"fs-id1167836423566\">\n<p id=\"fs-id1167836423568\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-076c2d31604317e655a23b68d59b025a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#48;&#114;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"170\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829696661\">In the following exercises, subtract the polynomials.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829696664\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829696666\">\n<p id=\"fs-id1167829696668\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c67012d37fedfecb6517b62d1df59c57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"69\" style=\"vertical-align: -7px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f078f925519c0f3b2ce7eac21897248b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"110\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167824584633\">\n<p id=\"fs-id1167824584635\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c6ef7e5b012fabc6ca88ced5ac11b219_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829620966\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829620969\">\n<p id=\"fs-id1167836650171\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5ecd11591872b1d3a71ec8218f7e5cbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#121;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"109\" style=\"vertical-align: -7px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fc2ffc499fe50e4b928482361243dfb2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#48;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#121;&#45;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"126\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836613921\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836613923\">\n<p id=\"fs-id1167836613925\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-aff128b690f34421a2c8bfe135b532da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#119;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"116\" style=\"vertical-align: -7px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c4d5e9082bc6d360ffb43759f65ec527_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#119;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"107\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829702031\">\n<p id=\"fs-id1167829702033\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f49690431fa7b9ac4f31778bb6a96ced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#119;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"95\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836615484\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836615486\">\n<p id=\"fs-id1167836615488\">Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f79934cc948e5f56878ff14467c75045_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"110\" style=\"vertical-align: -7px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e90310e5ea21eb5cbb577e1723b5570b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#120;&#45;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"119\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836666634\">In the following exercises, find the difference of the polynomials.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829717203\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829717206\">\n<p id=\"fs-id1167829717208\">Find the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0983d10a1d7ffc530bba5b7b4996aed7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#43;&#119;&#45;&#52;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"107\" style=\"vertical-align: -7px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-27ee1319202442f1f3c4856f18e95f05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#48;&#119;&#43;&#50;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"125\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167829589207\">\n<p id=\"fs-id1167829589209\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fe7942f01720f4cac2916ac3aa4e5bd3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#119;&#45;&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"70\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836531012\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836531014\">\n<p id=\"fs-id1167836531017\">Find the difference of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-77238d56ce78903cb71f53b607d8a688_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#122;&#45;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"108\" style=\"vertical-align: -7px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c7bb9533814ee285b71288d85dd4d9c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#122;&#45;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"108\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829931386\">In the following exercises, add the polynomials.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829931390\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829931392\">\n<p id=\"fs-id1167829931394\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d805b571c0939cad31e49cc59525ac73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#120;&#121;&#43;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"251\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836596754\">\n<p id=\"fs-id1167832981645\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-12a66c0d345378b3c387b8339c19c42e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#120;&#121;&#43;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"131\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836728252\">\n<p id=\"fs-id1167836728254\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5858248482cbf5c74ccded27cb68ef61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#120;&#121;&#45;&#51;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#120;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"265\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824740668\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167824740670\">\n<p id=\"fs-id1167824740672\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7d418c022ed09d0a4b7b7b5739c5f14a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#109;&#110;&#45;&#56;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#109;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"269\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836407251\">\n<p id=\"fs-id1167836484935\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-68da7607fbc0480d820db5f05a30e873_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#109;&#110;&#45;&#56;&#123;&#110;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"145\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836423638\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836423640\">\n<p id=\"fs-id1167836423642\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-28ef8bc3e423fadf16dd46a235818163_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#114;&#115;&#45;&#50;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#114;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"241\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167829742745\">In the following exercises, add or subtract the polynomials.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167829742748\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829742751\">\n<p id=\"fs-id1167829742753\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-286da9bc7056c23c57d498e0ba9c00f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#97;&#98;&#45;&#52;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"214\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833086321\">\n<p id=\"fs-id1167833086323\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ea6ca513485499f5b3069b1a3a28d644_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#97;&#98;&#43;&#51;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"84\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829787220\">\n<p id=\"fs-id1167829787222\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a668a7ef11692ce76b1fdc06324b6854_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#109;&#110;&#45;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"242\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829594307\" class=\"material-set-2\">\n<div data-type=\"problem\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8c30a3227f1d67b21ed6b00df0bd1fea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#45;&#51;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#113;&#43;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"322\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-161998e278e42454bedf5ecdcabfcea5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#45;&#54;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#113;&#43;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#123;&#113;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"166\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829750509\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829750511\">\n<p id=\"fs-id1167829750513\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-04d3357ae5f997a3c08412cfa0d19691_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#45;&#50;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#43;&#52;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"311\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829905295\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829905297\">\n<p id=\"fs-id1167829905299\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c258e1759d2b3ed23ec8e7b916a5bd54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#45;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"314\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836599533\">\n<p id=\"fs-id1167836599535\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-228ffc9c4225b2f1e0567e928e0b3b1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#45;&#53;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836629436\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836629438\">\n<p id=\"fs-id1167836629440\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9866de46df231ac4badb423c5e77b3f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#45;&#52;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"323\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167836432779\"><strong data-effect=\"bold\">Evaluate a Polynomial Function for a Given Value<\/strong><\/p>\n<p id=\"fs-id1167836432784\">In the following exercises, find the function values for each polynomial function.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836432788\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836432790\">\n<p>For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5e4ac8285488eab65a25b1605f28775a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#43;&#50;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"163\" style=\"vertical-align: -4px;\" \/> find:<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-00e628545709308df2fad3ec5e77a716_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-dca5d7bc047aaa23a5ac85a2c257c5f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"49\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3d73c012bc8b5a6f560bea30840502b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167832982231\">\n<p id=\"fs-id1167832982233\"><span class=\"token\">\u24d0<\/span> 187 <span class=\"token\">\u24d1<\/span> 40 <span class=\"token\">\u24d2<\/span> 2<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832982250\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167832982252\">\n<p id=\"fs-id1167836561341\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b8e3dd750746c8cfb8a6fd97108720a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#45;&#55;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"154\" style=\"vertical-align: -4px;\" \/> find:<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-93495ad7b580fb77c102c40fbc21a31f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"49\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-91ba6dcc1b657dfb8a4f15162ee96b42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3d73c012bc8b5a6f560bea30840502b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"35\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167829738632\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829738634\">\n<p id=\"fs-id1167829738637\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f55f67e8299f07a5d3de89cc83e3e889_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#45;&#51;&#54;&#120;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"122\" style=\"vertical-align: -4px;\" \/> find:<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e2adbcd4624c8f3e37ee45ba3f66530b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e3ee0ed7cf1ec152b02cf6c51c179b1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c180bd3dc0c2ee1eaf25f823f5a72c32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"48\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"solution\" id=\"fs-id1167832977153\">\n<p id=\"fs-id1167832977155\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-193855481ddfd218c0d96edfcd09b353_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/><span class=\"token\">\u24d1<\/span> 4 <span class=\"token\">\u24d2<\/span> 40<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836558053\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836558055\">\n<p id=\"fs-id1167836558057\">For the function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f982a716493441870d4e8c4730272634_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#49;&#54;&#45;&#51;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -4px;\" \/> find:<\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c180bd3dc0c2ee1eaf25f823f5a72c32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"48\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e3ee0ed7cf1ec152b02cf6c51c179b1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d2<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b42d35fe562a099584b3845d1d6c833c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"34\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<p id=\"fs-id1167824754903\">In the following exercises, find the height for each polynomial function.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836609191\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836609193\">\n<p id=\"fs-id1167836609196\">A painter drops a brush from a platform 75 feet high. The polynomial function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1de7bcdfd99e0219e4deb68afe5cf015_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" style=\"vertical-align: -4px;\" \/> gives the height of the brush <em data-effect=\"italics\">t<\/em> seconds after it was dropped. Find the height after <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-eec54adef7198c4decb9169a2b472009_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"38\" style=\"vertical-align: 0px;\" \/> seconds.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836423697\">\n<p id=\"fs-id1167836423699\">The height is 11 feet.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836333432\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836333434\">\n<p id=\"fs-id1167836333436\">A girl drops a ball off the cliff into the ocean. The polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-96d92093aebd2aee040cbb20657b471f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#92;&#108;&#101;&#102;&#116;&#40;&#116;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -4px;\" \/> gives the height of a ball <em data-effect=\"italics\">t<\/em> seconds after it is dropped. Find the height after <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0807de1d4e00db15c6d9ac7e73ae67b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\" \/> seconds.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824755607\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167824755609\">\n<p id=\"fs-id1167824755611\">A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of <em data-effect=\"italics\">p<\/em> dollars each is given by the polynomial function <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6a7c4eb503ac8c7fcad488925e3c2794_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#52;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#50;&#48;&#112;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"164\" style=\"vertical-align: -4px;\" \/> Find the revenue received when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ec105c20d5af31c346cfb014de3cc852_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -4px;\" \/> dollars.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836732114\">\n<p id=\"fs-id1167836732116\">The revenue is ?10,800.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836732122\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836732124\">\n<p id=\"fs-id1167836732126\">A manufacturer of the latest basketball shoes has found that the revenue received from selling the shoes at a cost of <em data-effect=\"italics\">p<\/em> dollars each is given by the polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6a7c4eb503ac8c7fcad488925e3c2794_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#82;&#92;&#108;&#101;&#102;&#116;&#40;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#52;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#50;&#48;&#112;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"164\" style=\"vertical-align: -4px;\" \/> Find the revenue received when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-68473c6e91d4ce8cac8c2109d41fe859_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#57;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"52\" style=\"vertical-align: -4px;\" \/> dollars.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833022467\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833022469\">\n<p id=\"fs-id1167833022472\">The polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7cefe602efae4b75f4c4fe89435939af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" style=\"vertical-align: -4px;\" \/> gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side <em data-effect=\"italics\">x<\/em> feet and height 6 feet. Find the cost of producing a box with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2145acc2878ed61214887e120f2485b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"43\" style=\"vertical-align: -1px;\" \/> feet.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833050568\">\n<p id=\"fs-id1167833050570\">The cost is ?456.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833050575\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167829695828\">\n<p id=\"fs-id1167829695830\">The polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7cefe602efae4b75f4c4fe89435939af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#67;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" style=\"vertical-align: -4px;\" \/> gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side <em data-effect=\"italics\">x<\/em> feet and height 4 feet. Find the cost of producing a box with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-116dfacb4c2a32bdfb5ab9e852f29986_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> feet.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167833381677\"><strong data-effect=\"bold\">Add and Subtract Polynomial Functions<\/strong><\/p>\n<p id=\"fs-id1167833381682\">In each example, find <span class=\"token\">\u24d0<\/span> (<em data-effect=\"italics\">f<\/em> + <em data-effect=\"italics\">g<\/em>)(<em data-effect=\"italics\">x<\/em>)\u2003<span class=\"token\">\u24d1<\/span> (<em data-effect=\"italics\">f<\/em> + <em data-effect=\"italics\">g<\/em>)(2)\u2003<span class=\"token\">\u24d2<\/span> (<em data-effect=\"italics\">f<\/em> \u2212 <em data-effect=\"italics\">g<\/em>)(<em data-effect=\"italics\">x<\/em>)\u2003<span class=\"token\">\u24d3<\/span> (<em data-effect=\"italics\">f<\/em> \u2212 <em data-effect=\"italics\">g<\/em>)(\u22123).<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167836418844\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836418846\">\n<p id=\"fs-id1167836418848\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-24f3f708ca8a1fa02f814955fba31c4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#120;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-76970a8af4133779b6706f86f7fec069_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167833086694\">\n<p id=\"fs-id1167833086696\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4c59448901291ff0b70bd737ebfce4a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"203\" style=\"vertical-align: -4px;\" \/><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b1b96e4692e0339fa97dba3580ec7cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-77d08856b69680eb57c7f0fb804945a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#50;&#120;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"224\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-609b04e886e4a3716e33e414a1211b61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"126\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167833347303\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167833347305\">\n<p id=\"fs-id1167833347308\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-dd01e6b6e321de95e014198f5952623d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"159\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fca82adddb851f6303bab1e826da0ade_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"157\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836624045\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167836624047\">\n<p id=\"fs-id1167836624049\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f8a5ea0de618a92759125a2c4ccb48d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"199\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-846bae0463cc922af0223d1f2dbfb0c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#51;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#55;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"127\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836409394\">\n<p id=\"fs-id1167836409396\">\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d0<\/span>&nbsp;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e3d2be9acb84eb539653964819854de4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#54;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"242\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c1e2b99c8fc832777e85305e6f7407e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#43;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d2<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2561e0d03140ed547a88cb54517bce3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#8722;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"194\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d3<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-fab8288234a12e44dc1c88aeb971e3c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#102;&#45;&#103;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#45;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"148\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824732288\" class=\"material-set-2\">\n<div data-type=\"problem\" id=\"fs-id1167824732290\">\n<p id=\"fs-id1167824732292\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-de45ee77b4f86c4977baa0b03d31c63f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#102;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"199\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6c480631bde54ed4e73b2e6cf44cdfd5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#103;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"writing\" data-depth=\"2\" id=\"fs-id1167836529231\">\n<h4 data-type=\"title\">Writing Exercises<\/h4>\n<div data-type=\"exercise\" id=\"fs-id1167836529238\">\n<div data-type=\"problem\" id=\"fs-id1167836529240\">\n<p id=\"fs-id1167836529242\">Using your own words, explain the difference between a monomial, a binomial, and a trinomial.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836529248\">\n<p id=\"fs-id1167836529250\">Answers will vary.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167836529255\">\n<div data-type=\"problem\" id=\"fs-id1167836618900\">\n<p id=\"fs-id1167836618902\">Using your own words, explain the difference between a polynomial with five terms and a polynomial with a degree of 5.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167836618917\">\n<p id=\"fs-id1167836618919\">Ariana thinks the sum <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5de90ad6748f719cb7c52581c236d4d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#123;&#121;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -4px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-94549982b41bebc03eb941310d1258cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#123;&#121;&#125;&#94;&#123;&#54;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -4px;\" \/> What is wrong with her reasoning?<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167836494401\">\n<p id=\"fs-id1167836494403\">Answers will vary.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167824755444\">\n<div data-type=\"problem\" id=\"fs-id1167824755447\">\n<p id=\"fs-id1167824755449\">Is every trinomial a second degree polynomial? If not, give an example.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167824755462\">\n<h4 data-type=\"title\">Self Check<\/h4>\n<p id=\"fs-id1167824755467\"><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167836602621\" data-alt=\"The figure shows a table with six rows and four columns. The first row is a header row and it labels each column. The first column header is \u201cI can\u2026\u201d, the second is &quot;confidently&quot;, the third is \u201cwith some help\u201d, \u201cno minus I don\u2019t get it!\u201d. Under the first column are the phrases \u201cidentify polynomials, monomials, binomials, and trinomials\u201d, \u201cdetermine the degree of polynomials\u201d, \u201cadd and subtract monomials\u201d, \u201cadd and subtract polynomials\u201d, and \u201cevaluate a polynomial for a given value\u201d. Under the second, third, fourth columns are blank spaces where the learner can check what level of mastery they have achieved.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_05_01_201_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"The figure shows a table with six rows and four columns. The first row is a header row and it labels each column. The first column header is \u201cI can\u2026\u201d, the second is &quot;confidently&quot;, the third is \u201cwith some help\u201d, \u201cno minus I don\u2019t get it!\u201d. Under the first column are the phrases \u201cidentify polynomials, monomials, binomials, and trinomials\u201d, \u201cdetermine the degree of polynomials\u201d, \u201cadd and subtract monomials\u201d, \u201cadd and subtract polynomials\u201d, and \u201cevaluate a polynomial for a given value\u201d. Under the second, third, fourth columns are blank spaces where the learner can check what level of mastery they have achieved.\" \/><\/span><\/p>\n<p id=\"fs-id1167836602631\"><span class=\"token\">\u24d1<\/span> If most of your checks were:<\/p>\n<p id=\"fs-id1167836602638\"><strong data-effect=\"bold\">\u2026confidently.<\/strong> Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.<\/p>\n<p id=\"fs-id1167829767167\"><strong data-effect=\"bold\">\u2026with some help.<\/strong> This must be addressed quickly because topics you do not master become potholes in your road to success. In math every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?<\/p>\n<p id=\"fs-id1167829767178\"><strong data-effect=\"bold\">\u2026no &#8211; I don\u2019t get it!<\/strong> This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h3 data-type=\"glossary-title\">Glossary<\/h3>\n<dl id=\"fs-id1167836508735\">\n<dt>binomial<\/dt>\n<dd id=\"fs-id1167836508741\">A binomial is a polynomial with exactly two terms.<\/dd>\n<\/dl>\n<dl id=\"fs-id1167836508745\">\n<dt>degree of a constant<\/dt>\n<dd id=\"fs-id1167836508750\">The degree of any constant is 0.<\/dd>\n<\/dl>\n<dl id=\"fs-id1167836508755\">\n<dt>degree of a polynomial<\/dt>\n<dd id=\"fs-id1167836508760\">The degree of a polynomial is the highest degree of all its terms.<\/dd>\n<\/dl>\n<dl id=\"fs-id1167836508764\">\n<dt>degree of a term<\/dt>\n<dd id=\"fs-id1167833385664\">The degree of a term is the sum of the exponents of its variables.<\/dd>\n<\/dl>\n<dl id=\"fs-id1167833385668\">\n<dt>monomial<\/dt>\n<dd id=\"fs-id1167833385674\">A monomial is an algebraic expression with one term. A monomial in one variable is a term of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f8fe74b3bd004d025e1a2dce9b428a1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#123;&#120;&#125;&#94;&#123;&#109;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"36\" style=\"vertical-align: -4px;\" \/> where <em data-effect=\"italics\">a<\/em> is a constant and <em data-effect=\"italics\">m<\/em> is a whole number.<\/dd>\n<\/dl>\n<dl id=\"fs-id1167829853744\">\n<dt>polynomial<\/dt>\n<dd id=\"fs-id1167829853749\">A monomial or two or more monomials combined by addition or subtraction is a polynomial.<\/dd>\n<\/dl>\n<dl id=\"fs-id1167829853754\">\n<dt>standard form of a polynomial<\/dt>\n<dd id=\"fs-id1167829853760\">A polynomial is in standard form when the terms of a polynomial are written in descending order of degrees.<\/dd>\n<\/dl>\n<dl id=\"fs-id1167833350539\">\n<dt>trinomial<\/dt>\n<dd id=\"fs-id1167833350544\">A trinomial is a polynomial with exactly three terms.<\/dd>\n<\/dl>\n<dl id=\"fs-id1167833350548\">\n<dt>polynomial function<\/dt>\n<dd id=\"fs-id1167833350554\">A polynomial function is a function whose range values are defined by a polynomial.<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":103,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2775","chapter","type-chapter","status-publish","hentry"],"part":2727,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/2775","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/users\/103"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/2775\/revisions"}],"predecessor-version":[{"id":15238,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/2775\/revisions\/15238"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/parts\/2727"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/2775\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/media?parent=2775"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapter-type?post=2775"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/contributor?post=2775"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/license?post=2775"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}