{"id":1685,"date":"2021-05-19T16:45:17","date_gmt":"2021-05-19T16:45:17","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/add-and-subtract-polynomials\/"},"modified":"2023-06-26T03:40:19","modified_gmt":"2023-06-26T03:40:19","slug":"add-and-subtract-polynomials","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/add-and-subtract-polynomials\/","title":{"raw":"6.1 Add and Subtract Polynomials","rendered":"6.1 Add and Subtract Polynomials"},"content":{"raw":"[latexpage]\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Identify polynomials, monomials, binomials, and trinomials<\/li>\r\n \t<li>Determine the degree of polynomials<\/li>\r\n \t<li>Add and subtract monomials<\/li>\r\n \t<li>Add and subtract polynomials<\/li>\r\n \t<li>Evaluate a polynomial for a given value<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<h1>Identify Polynomials, Monomials, Binomials and Trinomials<\/h1>\r\n<p id=\"fs-id1169596310635\">You have learned that a <em data-effect=\"italics\">term<\/em> is a constant or the product of a constant and one or more variables. When it is of the form \\(a{x}^{m}\\), where \\(a\\) is a constant and \\(m\\) is a whole number, it is called a monomial. Some examples of monomial are \\(8,-2{x}^{2},4{y}^{3}\\), and \\(11{z}^{7}\\).<\/p>\r\n\r\n<div id=\"fs-id1169596365842\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Monomials<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA monomial is a term of the form \\(a{x}^{m}\\), where \\(a\\) is a constant and \\(m\\) is a positive whole number.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169596286467\">A monomial, or two or more monomials combined by addition or subtraction, is a polynomial. 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 trinomial has exactly three terms. There are no special names for polynomials with more than three terms.<\/p>\r\n\r\n<div id=\"fs-id1169596312244\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Polynomials<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1168745072439\">polynomial\u2014A monomial, or two or more monomials combined by addition or subtraction, is a polynomial.<\/p>\r\n\r\n<ul id=\"fs-id1169596372377\" data-bullet-style=\"open-circle\">\r\n \t<li><strong data-effect=\"bold\">monomial<\/strong>\u2014A polynomial with exactly one term is called a monomial.<\/li>\r\n \t<li><strong>binomial<\/strong>\u2014A polynomial with exactly two terms is called a binomial.<\/li>\r\n \t<li><strong>trinomial<\/strong>\u2014A polynomial with exactly three terms is called a trinomial.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169596360597\">Here are some examples of polynomials.<\/p>\r\n<p id=\"fs-id1169596286034\">\\(\\begin{array}{lllll}\\text{Polynomial} &amp; b+1 &amp; 4{y}^{2}-7y+2 \\qquad &amp; 4{x}^{4}+{x}^{3}+8{x}^{2}-9x+1&amp;\\\\ \\text{Monomial}&amp; 14&amp; 8{y}^{2} &amp; -9{x}^{3}{y}^{5} &amp; -13 \\\\ \\text{Binomial} &amp;a+7&amp; 4b-5 &amp; {y}^{2}-16 &amp; 3{x}^{3}-9{x}^{2} \\\\ \\text{Trinomial} &amp; {x}^{2}-7x+12 \\qquad &amp; 9{y}^{2}+2y-8 \\qquad &amp; 6{m}^{4}-{m}^{3}+8m &amp; {z}^{4}+3{z}^{2}-1\\hfill \\end{array}\\)<\/p>\r\n<p id=\"fs-id1169596281141\">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>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596499092\" data-type=\"problem\">\r\n<p id=\"fs-id1169596254275\">Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial.<\/p>\r\n\r\n<ol id=\"fs-id1168745110296\" class=\"circled\" type=\"a\">\r\n \t<li>\\(4{y}^{2}-8y-6\\)<\/li>\r\n \t<li>\\(-5{a}^{4}{b}^{2}\\)<\/li>\r\n \t<li>\\(2{x}^{5}-5{x}^{3}-9{x}^{2}+3x+4\\)<\/li>\r\n \t<li>\\(13-5{m}^{3}\\)<\/li>\r\n \t<li>\\(q\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1169596386484\" data-type=\"solution\">\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-163\" class=\"grid\" summary=\"\/\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><strong>Polynomial<\/strong><\/td>\r\n<td><strong>Number of terms<\/strong><\/td>\r\n<td><strong>Type<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>a)<\/td>\r\n<td>\\(4{y}^{2}-8y-6\\)<\/td>\r\n<td>\\(3\\)<\/td>\r\n<td>Trinomial<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b)<\/td>\r\n<td>\\(-5{a}^{4}{b}^{2}\\)<\/td>\r\n<td>\\(1\\)<\/td>\r\n<td>Monomial<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>c)<\/td>\r\n<td>\\(2{x}^{5}-5{x}^{3}-9{x}^{2}+3x+4\\)<\/td>\r\n<td>\\(5\\)<\/td>\r\n<td>Polynomial<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>d)<\/td>\r\n<td>\\(13-5{m}^{3}\\)<\/td>\r\n<td>\\(2\\)<\/td>\r\n<td>Binomial<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>e)<\/td>\r\n<td>\\(q\\)<\/td>\r\n<td>\\(1\\)<\/td>\r\n<td>Monomial<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596404492\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596319079\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596319081\" data-type=\"problem\">\r\n<p id=\"fs-id1169596319083\">Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial:<\/p>\r\n<p id=\"fs-id1168745401854\">a) \\(5b\\) b) \\(8{y}^{3}-7{y}^{2}-y-3\\) c) \\(-3{x}^{2}-5x+9\\) d) \\(81-4{a}^{2}\\)e)\\(-5{x}^{6}\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596497627\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596497629\">a) monomial b) polynomial c) trinomial d) binomial e) monomial<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596399868\" data-type=\"problem\">\r\n<p id=\"fs-id1169596399870\">Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial:<\/p>\r\n<p id=\"fs-id1168745201798\">a) \\(27{z}^{3}-8\\) b) \\(12{m}^{3}-5{m}^{2}-2m\\) c) \\(\\dfrac{5}{6}\\) d) \\(8{x}^{4}-7{x}^{2}-6x-5\\) e) \\(-{n}^{4}\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596369494\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596369496\">a) binomial b) trinomial c) monomial d) polynomial e) monomial<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Determine the Degree of Polynomials<\/h1>\r\n<p id=\"fs-id1169596369612\">The degree of a polynomial and the degree of its terms are determined by the exponents of the variable.<\/p>\r\n<p id=\"fs-id1169596369616\">A <span class=\"no-emphasis\" data-type=\"term\">monomial<\/span> that has no variable, just a constant, is a special case. The degree of a constant is 0\u2014it has no variable.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Degree of a Polynomial<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1169596369626\">The degree of a term is the sum of the exponents of its variables.<\/p>\r\n<p id=\"fs-id1169596373156\">The degree of a constant is 0.<\/p>\r\n<p id=\"fs-id1169596373162\">The degree of a polynomial is the highest degree of all its terms.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169596373170\">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>\r\n<span id=\"fs-id1169596498644\" data-type=\"media\" data-alt=\"This table has 11 rows and 5 columns. The first column is a header column, and it names each row. The first row is named \u201cMonomial,\u201d and each cell in this row contains a different monomial. The second row is named \u201cDegree,\u201d and each cell in this row contains the degree of the monomial above it. The degree of 14 is 0, the degree of 8y squared is 2, the degree of negative 9x cubed y to the fifth power is 8, and the degree of negative 13a is 1. The third row is named \u201cBinomial,\u201d and each cell in this row contains a different binomial. The fourth row is named \u201cDegree of each term,\u201d and each cell contains the degrees of the two terms in the binomial above it. The fifth row is named \u201cDegree of polynomial,\u201d and each cell contains the degree of the binomial as a whole.\u201d The degrees of the terms in a plus 7 are 0 and 1, and the degree of the whole binomial is 1. The degrees of the terms in 4b squared minus 5b are 2 and 1, and the degree of the whole binomial is 2. The degrees of the terms in x squared y squared minus 16 are 4 and 0, and the degree of the whole binomial is 4. The degrees of the terms in 3n cubed minus 9n squared are 3 and 2, and the degree of the whole binomial is 3. The sixth row is named \u201cTrinomial,\u201d and each cell in this row contains a different trinomial. The seventh row is named \u201cDegree of each term,\u201d and each cell contains the degrees of the three terms in the trinomial above it. The eighth row is named \u201cDegree of polynomial,\u201d and each cell contains the degree of the trinomial as a whole. The degrees of the terms in x squared minus 7x plus 12 are 2, 1, and 0, and the degree of the whole trinomial is 2. The degrees of the terms in 9a squared plus 6ab plus b squared are 2, 2, and 2, and the degree of the trinomial as a whole is 2. The degrees of the terms in 6m to the fourth power minus m cubed n squared plus 8mn to the fifth power are 4, 5, and 6, and the degree of the whole trinomial is 6. The degrees of the terms in z to the fourth power plus 3z squared minus 1 are 4, 2, and 0, and the degree of the whole trinomial is 4. The ninth row is named \u201cPolynomial,\u201d and each cell contains a different polynomial. The tenth row is named \u201cDegree of each term,\u201d and the eleventh row is named \u201cDegree of polynomial.\u201d The degrees of the terms in b plus 1 are 1 and 0, and the degree of the whole polynomial is 1. The degrees of the terms in 4y squared minus 7y plus 2 are 2, 1, and 0, and the degree of the whole polynomial is 2. The degrees of the terms in 4x to the fourth power plus x cubed plus 8x squared minus 9x plus 1 are 4, 3, 2, 1, and 0, and the degree of the whole polynomial is 4.\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/CNX_ElemAlg_Figure_06_01_001_img_new.jpg\" alt=\"This table has 11 rows and 5 columns. The first column is a header column, and it names each row. The first row is named \u201cMonomial,\u201d and each cell in this row contains a different monomial. The second row is named \u201cDegree,\u201d and each cell in this row contains the degree of the monomial above it. The degree of 14 is 0, the degree of 8y squared is 2, the degree of negative 9x cubed y to the fifth power is 8, and the degree of negative 13a is 1. The third row is named \u201cBinomial,\u201d and each cell in this row contains a different binomial. The fourth row is named \u201cDegree of each term,\u201d and each cell contains the degrees of the two terms in the binomial above it. The fifth row is named \u201cDegree of polynomial,\u201d and each cell contains the degree of the binomial as a whole.\u201d The degrees of the terms in a plus 7 are 0 and 1, and the degree of the whole binomial is 1. The degrees of the terms in 4b squared minus 5b are 2 and 1, and the degree of the whole binomial is 2. The degrees of the terms in x squared y squared minus 16 are 4 and 0, and the degree of the whole binomial is 4. The degrees of the terms in 3n cubed minus 9n squared are 3 and 2, and the degree of the whole binomial is 3. The sixth row is named \u201cTrinomial,\u201d and each cell in this row contains a different trinomial. The seventh row is named \u201cDegree of each term,\u201d and each cell contains the degrees of the three terms in the trinomial above it. The eighth row is named \u201cDegree of polynomial,\u201d and each cell contains the degree of the trinomial as a whole. The degrees of the terms in x squared minus 7x plus 12 are 2, 1, and 0, and the degree of the whole trinomial is 2. The degrees of the terms in 9a squared plus 6ab plus b squared are 2, 2, and 2, and the degree of the trinomial as a whole is 2. The degrees of the terms in 6m to the fourth power minus m cubed n squared plus 8mn to the fifth power are 4, 5, and 6, and the degree of the whole trinomial is 6. The degrees of the terms in z to the fourth power plus 3z squared minus 1 are 4, 2, and 0, and the degree of the whole trinomial is 4. The ninth row is named \u201cPolynomial,\u201d and each cell contains a different polynomial. The tenth row is named \u201cDegree of each term,\u201d and the eleventh row is named \u201cDegree of polynomial.\u201d The degrees of the terms in b plus 1 are 1 and 0, and the degree of the whole polynomial is 1. The degrees of the terms in 4y squared minus 7y plus 2 are 2, 1, and 0, and the degree of the whole polynomial is 2. The degrees of the terms in 4x to the fourth power plus x cubed plus 8x squared minus 9x plus 1 are 4, 3, 2, 1, and 0, and the degree of the whole polynomial is 4.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1169596498652\">A polynomial is in standard form when the terms of a polynomial are written in descending order of degrees. Get in the habit of writing the term with the highest degree first.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596396659\" data-type=\"problem\">\r\n<p id=\"fs-id1169596396661\">Find the degree of the following polynomials.<\/p>\r\n\r\n<ol id=\"fs-id1168745374893\" class=\"circled\" type=\"a\">\r\n \t<li>\\(10y\\)<\/li>\r\n \t<li>\\(4{x}^{3}-7x+5\\)<\/li>\r\n \t<li>\\(-15\\)<\/li>\r\n \t<li>\\(-8{b}^{2}+9b-2\\)<\/li>\r\n \t<li>\\(8x{y}^{2}+2y\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1169596374685\" data-type=\"solution\">\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-712\" class=\"grid\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>a)\r\nThe exponent of \\(y\\) is one. \\(y={y}^{1}\\)<\/td>\r\n<td>\\(10y\\)\r\nThe degree is 1.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b)\r\nThe highest degree of all the terms is 3.<\/td>\r\n<td>\\(4{x}^{3}-7x+5\\)\r\nThe degree is 3.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>c)\r\nThe degree of a constant is 0.<\/td>\r\n<td>\\(-15\\)\r\nThe degree is 0.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>d)\r\nThe highest degree of all the terms is 2.<\/td>\r\n<td>\\(-8{b}^{2}+9b-2\\)\r\nThe degree is 2.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>e)\r\nThe highest degree of all the terms is 3.<\/td>\r\n<td>\\(8x{y}^{2}+2y\\)\r\nThe degree is 3.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 2.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596500767\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596500770\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596500772\" data-type=\"problem\">\r\n<p id=\"fs-id1169596500774\">Find the degree of the following polynomials:<\/p>\r\n<p id=\"fs-id1168742186774\">a) \\(-15b\\) b) \\(10{z}^{4}+4{z}^{2}-5\\) c) \\(12{c}^{5}{d}^{4}+9{c}^{3}{d}^{9}-7\\) d) \\(3{x}^{2}y-4x\\)e)\\(-9\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596316182\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596316184\">a) \\(1\\) b) \\(4\\) c) \\(12\\) d) 3 e) 0<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596372752\" data-type=\"problem\">\r\n<p id=\"fs-id1169596372754\">Find the degree of the following polynomials:<\/p>\r\n<p id=\"fs-id1168742143930\">a) \\(52\\) b) \\({a}^{4}b-17{a}^{4}\\) c) \\(5x+6y+2z\\) d) \\(3{x}^{2}-5x+7\\)e)\\(-{a}^{3}\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596396979\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596396981\">a) \\(0\\) b) \\(5\\) c) \\(1\\) d) 2 e) 3<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Add and Subtract Monomials<\/h1>\r\n<p id=\"fs-id1169596396811\">You 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 coefficient.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596396821\" data-type=\"problem\">\r\n<p id=\"fs-id1169596396824\">Add: \\(25{y}^{2}+15{y}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596370510\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-960\" summary=\"\/\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(25{y}^{2}+15{y}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>\\(40{y}^{2}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596258575\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596258578\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596258581\" data-type=\"problem\">\r\n<p id=\"fs-id1169596258583\">Add: \\(12{q}^{2}+9{q}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596497124\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596497126\">\\(21{q}^{2}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY 3.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596497146\" data-type=\"problem\">\r\n<p id=\"fs-id1169596497148\">Add: \\(-15{c}^{2}+8{c}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596401651\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596401653\">\\(-7{c}^{2}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596497141\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596497144\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596401651\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596499322\" data-type=\"problem\">\r\n<p id=\"fs-id1169596499325\">Subtract: \\(16p-\\left(-7p\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596499349\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-187\" class=\"unnumbered unstyled\" summary=\"\/\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(16p-\\left(-7p\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>\\(23p\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596410075\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596410078\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596410080\" data-type=\"problem\">\r\n<p id=\"fs-id1169596410083\">Subtract: \\(8m-\\left(-5m\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596410106\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596410108\">\\(13m\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596499254\" data-type=\"problem\">\r\n<p id=\"fs-id1169596499257\">Subtract: \\(-15{z}^{3}-\\left(-5{z}^{3}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596499286\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596499289\">\\(-10{z}^{3}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1169596453975\">Remember that like terms must have the same variables with the same exponents.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596453982\" data-type=\"problem\">\r\n<p id=\"fs-id1169596453984\">Simplify: \\({c}^{2}+7{d}^{2}-6{c}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596454016\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-477\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\({c}^{2}+7{d}^{2}-6{c}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>\\(-5{c}^{2}+7{d}^{2}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596498346\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596498349\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596498351\" data-type=\"problem\">\r\n<p id=\"fs-id1169596498353\">Add: \\(8{y}^{2}+3{z}^{2}-3{y}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596308850\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596308853\">\\(5{y}^{2}+3{z}^{2}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596308882\" data-type=\"problem\">\r\n<p id=\"fs-id1169596308885\">Add: \\(3{m}^{2}+{n}^{2}-7{m}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596499692\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596499694\">\\(-4{m}^{2}+{n}^{2}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596308877\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596308880\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596499692\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596499721\" data-type=\"problem\">\r\n<p id=\"fs-id1169596499723\">Simplify: \\({u}^{2}v+5{u}^{2}-3{v}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596360371\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-77\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\({u}^{2}v+5{u}^{2}-3{v}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>There are no like terms to combine.<\/td>\r\n<td>\\({u}^{2}v+5{u}^{2}-3{v}^{2}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596499224\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596499228\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596499230\" data-type=\"problem\">\r\n<p id=\"fs-id1169596499232\">Simplify: \\({m}^{2}{n}^{2}-8{m}^{2}+4{n}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596362274\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596362277\">There are no like terms to combine.<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596362288\" data-type=\"problem\">\r\n<p id=\"fs-id1169596362290\">Simplify: \\(p{q}^{2}-6p-5{q}^{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596453918\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596453920\">There are no like terms to combine.<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596308880\" data-type=\"exercise\"><\/div>\r\n<\/div>\r\n<h1>Add and Subtract Polynomials<\/h1>\r\nWe 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.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596453948\" data-type=\"problem\">\r\n<p id=\"fs-id1169596453950\">Find the sum: \\(\\left(5{y}^{2}-3y+15\\right)+\\left(3{y}^{2}-4y-11\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596497918\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\">\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 25.4417%\">Identify like terms.<\/td>\r\n<td style=\"width: 74.5583%\">[latex](\\underline{\\underline{5y^2}}-\\underline{3y} \\color{red}{+15})[\/latex] + [latex](\\underline{\\underline{3y^2}}-\\underline{4y} \\color{red}{-11})[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 25.4417%\">Rearrange to get the like terms together.<\/td>\r\n<td style=\"width: 74.5583%\">[latex]\\underline{\\underline{5y^2+ 3y^2}}-\\underline{3y-4y} \\color{red}{+15-11}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 25.4417%\">Combine like terms.<\/td>\r\n<td style=\"width: 74.5583%\">[latex]8y^2-7y+4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596378229\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596378233\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596378235\" data-type=\"problem\">\r\n<p id=\"fs-id1169596378237\">Find the sum: \\(\\left(7{x}^{2}-4x+5\\right)+\\left({x}^{2}-7x+3\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596499124\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596499127\">\\(8{x}^{2}-11x+8\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596499158\" data-type=\"problem\">\r\n<p id=\"fs-id1169596499161\">Find the sum: \\(\\left(14{y}^{2}+6y-4\\right)+\\left(3{y}^{2}+8y+5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596497040\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596497042\">\\(17{y}^{2}+14y+1\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596499152\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596499156\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596497040\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596365153\" data-type=\"problem\">\r\n<p id=\"fs-id1169596365155\">Find the difference: \\(\\left(9{w}^{2}-7w+5\\right)-\\left(2{w}^{2}-4\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596365206\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1168745128145\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains the sum of two polynomials: 9w squared minus 7w plus 5, and 2w squared minus 4. One row down, the text in the left column says \u201cDistribute and identify like terms.\u201d The right column contains 9w squared minus 7w plus 5 minus 2w squared plus 4. 9w squared and 2w squared are identified as like terms. 5 and 4 are also identified as like terms. One row down, the text in the left column says \u201cRearrange the terms.\u201d The right column contains the earlier expression reordered so that like terms are grouped together: 9w squared minus 2w squared minus 7w plus 4 plus 4. One row down, the text in the left column says \u201cCombine like terms.\u201d The right column contains 7w squared minus 7w plus 9.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\left(9 w^2-7 w+5\\right)-\\left(2 w^2-4\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute and identify like terms.<\/td>\r\n<td><span id=\"eip-id1168741741686\" data-type=\"media\" data-alt=\"9 w squared and 2 w squared are like terms. 5 and 4 are also like terms.\">[latex]\\underline{\\underline{9 w^2}}-\\underline{7 w}+\\underset{\\sim}{5}-\\underline{\\underline{2 w^2}}+\\underset{\\sim}{4}[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rearrange the terms.<\/td>\r\n<td data-align=\"left\"><span id=\"eip-id1168745057880\" data-type=\"media\" data-alt=\"9 w squared minus 2 w squared minus 7 w plus 5 plus 4.\">[latex]\\underline{\\underline{9 w^2-2 w^2}} - \\underline{7 w}+\\underset{\\sim}{5}+\\underset{\\sim}{4}[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td><span id=\"eip-id1168745128259\" data-type=\"media\" data-alt=\"7 w squared minus 7 w plus 9.\">[latex]7 w^2-7 w+9[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596397950\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596397954\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596397956\" data-type=\"problem\">\r\n<p id=\"fs-id1169596397958\">Find the difference: \\(\\left(8{x}^{2}+3x-19\\right)-\\left(7{x}^{2}-14\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596360700\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596360702\">\\({x}^{2}+3x-5\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596360734\" data-type=\"problem\">\r\n<p id=\"fs-id1169596360736\">Find the difference: \\(\\left(9{b}^{2}-5b-4\\right)-\\left(3{b}^{2}-5b-7\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596496962\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596496964\">\\(6{b}^{2}+3\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596360727\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596360731\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596496962\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596496988\" data-type=\"problem\">\r\n<p id=\"fs-id1169596496990\">Subtract: \\(\\left({c}^{2}-4c+7\\right)\\) from \\(\\left(7{c}^{2}-5c+3\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596499471\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1172187783971\" class=\"unnumbered unstyled\" style=\"height: 84px;width: 930px\" summary=\"This figure has two columns. At the top of the figure, the right column contains the difference of two trinomials: 7c squared minus 5c plus 3, minus c squared minus 4c plus 7. One row down, the text in the left column says \u201cDistribute and identify like terms.\u201d The right column contains7c squared minus 5c plus 3 minus c squared plus 4c minus 7. 7c squared and c squared are identified as like terms. Minus 5c and 4c are also identified as like terms. 3 and minus 7 are identified as like terms as well. One row down, the text in the left column says \u201cRearrange the terms.\u201d The right column contains the earlier expression reordered so that like terms are grouped together: 7c squared minus c squared minus 5c plus 4c plus 3 minus 7. One row down, the text in the left column says \u201cCombine like terms.\u201d The right column contains 6c squared minus c minus 4.\" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 16px\">\r\n<td style=\"height: 16px;width: 432.597px\">Subtract: \\(\\left({c}^{2}-4c+7\\right)\\) from \\(\\left(7{c}^{2}-5c+3\\right)\\).<\/td>\r\n<td style=\"height: 16px;width: 467.46px\">[latex]\\left(7 c^2-5 c+3\\right)-\\left(c^2-4 c+7\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 25px\">\r\n<td style=\"height: 25px;width: 432.597px\">Distribute and identify like terms.<\/td>\r\n<td style=\"height: 25px;width: 467.46px\">[latex]\\underline{\\underline{7 c^2}}-\\underline{5 c}+\\underset{\\sim}{3}-\\underline{\\underline{c^2}}+\\underline{4 c}-\\underset{\\sim}{7}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 25px\">\r\n<td style=\"height: 25px;width: 432.597px\">Rearrange the terms.<\/td>\r\n<td style=\"height: 25px;width: 467.46px\" data-align=\"left\">[latex]\\underline{\\underline{7 c^2-c^2}}-\\underline{5 c+4 c}+\\underset{\\sim}{3}-\\underset{\\sim}{7}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 18px\">\r\n<td style=\"height: 18px;width: 432.597px\">Combine like terms.<\/td>\r\n<td style=\"height: 18px;width: 467.46px\"><span id=\"eip-id1172187784063\" data-type=\"media\" data-alt=\"6 c squared minus c minus 4.\">[latex]6 c^2-c-4[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596499488\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596391066\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596391069\" data-type=\"problem\">\r\n<p id=\"fs-id1169596391071\">Subtract: \\(\\left(5{z}^{2}-6z-2\\right)\\) from \\(\\left(7{z}^{2}+6z-4\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596391129\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596391132\">\\(2{z}^{2}+12z-2\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596407608\" data-type=\"problem\">\r\n<p id=\"fs-id1169596407610\">Subtract: \\(\\left({x}^{2}-5x-8\\right)\\) from \\(\\left(6{x}^{2}+9x-1\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596362987\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596362989\">\\(5{x}^{2}+14x+7\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596407602\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596407606\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596362987\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596363019\" data-type=\"problem\">\r\n<p id=\"fs-id1169596363021\">Find the sum: \\(\\left({u}^{2}-6uv+5{v}^{2}\\right)+\\left(3{u}^{2}+2uv\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596403189\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-135\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\left({u}^{2}-6uv+5{v}^{2}\\right)+\\left(3{u}^{2}+2uv\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>\\({u}^{2}-6uv+5{v}^{2}+3{u}^{2}+2uv\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rearrange the terms, to put like terms together.<\/td>\r\n<td>\\({u}^{2}+3{u}^{2}-6uv+2uv+5{v}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>\\(4{u}^{2}-4uv+5{v}^{2}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 10.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596370437\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596370441\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596370443\" data-type=\"problem\">\r\n<p id=\"fs-id1169596370446\">Find the sum: \\(\\left(3{x}^{2}-4xy+5{y}^{2}\\right)+\\left(2{x}^{2}-xy\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596388052\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596388054\">\\(5{x}^{2}-5xy+5{y}^{2}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 10.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596388094\" data-type=\"problem\">\r\n<p id=\"fs-id1169596388096\">Find the sum: \\(\\left(2{x}^{2}-3xy-2{y}^{2}\\right)+\\left(5{x}^{2}-3xy\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596399239\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596399242\">\\(7{x}^{2}-6xy-2{y}^{2}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596388087\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596388091\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596399239\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 11.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596366973\" data-type=\"problem\">\r\n<p id=\"fs-id1169596366975\">Find the difference: \\(\\left({p}^{2}+{q}^{2}\\right)-\\left({p}^{2}+10pq-2{q}^{2}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596367033\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-574\" class=\"unnumbered unstyled\" summary=\"\/\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\left({p}^{2}+{q}^{2}\\right)-\\left({p}^{2}+10pq-2{q}^{2}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>\\({p}^{2}+{q}^{2}-{p}^{2}-10pq+2{q}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rearrange the terms, to put like terms together.<\/td>\r\n<td>\\({p}^{2}-{p}^{2}-10pq+{q}^{2}+2{q}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>\\(-10p{q}^{2}+3{q}^{2}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596386709\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596386713\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596386715\" data-type=\"problem\">\r\n<p id=\"fs-id1169596386717\">Find the difference: \\(\\left({a}^{2}+{b}^{2}\\right)-\\left({a}^{2}+5ab-6{b}^{2}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596395647\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596395649\">\\(-5ab+7{b}^{2}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596395678\" data-type=\"problem\">\r\n<p id=\"fs-id1169596395681\">Find the difference: \\(\\left({m}^{2}+{n}^{2}\\right)-\\left({m}^{2}-7mn-3{n}^{2}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596389120\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596389122\">\\(4{n}^{2}+7mn\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596395672\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596395676\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596389120\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596389149\" data-type=\"problem\">\r\n<p id=\"fs-id1169596389152\">Simplify: \\(\\left({a}^{3}-{a}^{2}b\\right)-\\left(a{b}^{2}+{b}^{3}\\right)+\\left({a}^{2}b+a{b}^{2}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596362553\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-155\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\left({a}^{3}-{a}^{2}b\\right)-\\left(a{b}^{2}+{b}^{3}\\right)+\\left({a}^{2}b+a{b}^{2}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>\\({a}^{3}-{a}^{2}b-a{b}^{2}-{b}^{3}+{a}^{2}b+a{b}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rearrange the terms, to put like terms together.<\/td>\r\n<td>\\({a}^{3}-{a}^{2}b+{a}^{2}b-a{b}^{2}+a{b}^{2}-{b}^{3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>\\({a}^{3}-{b}^{3}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596387795\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596387799\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596387801\" data-type=\"problem\">\r\n<p id=\"fs-id1169596387803\">Simplify: \\(\\left({x}^{3}-{x}^{2}y\\right)-\\left(x{y}^{2}+{y}^{3}\\right)+\\left({x}^{2}y+x{y}^{2}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596319562\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596319564\">\\({x}^{3}-{y}^{3}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596319585\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596498186\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596498188\" data-type=\"problem\">\r\n<p id=\"fs-id1169596498190\">Simplify: \\(\\left({p}^{3}-{p}^{2}q\\right)+\\left(p{q}^{2}+{q}^{3}\\right)-\\left({p}^{2}q+p{q}^{2}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596398250\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596398252\">\\({p}^{3}-2{p}^{2}q+{q}^{3}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596389120\" data-type=\"solution\"><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Evaluate a Polynomial for a Given Value<\/h1>\r\n<p id=\"fs-id1169596398290\">We have already learned how to evaluate expressions. Since polynomials are expressions, we\u2019ll follow the same procedures to evaluate a <span class=\"no-emphasis\" data-type=\"term\">polynomial<\/span>. We will substitute the given value for the variable and then simplify using the order of operations.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nEvaluate \\(5{x}^{2}-8x+4\\) when\r\n<div id=\"fs-id1169596398304\" data-type=\"problem\">\r\n<ol id=\"fs-id1168741804270\" class=\"circled\" type=\"a\">\r\n \t<li>\\(x=4\\)<\/li>\r\n \t<li>\\(x=-2\\)<\/li>\r\n \t<li>\\(x=0\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1169596362926\" data-type=\"solution\">\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1168744362498\" class=\"unnumbered unstyled\" style=\"width: 1134px;height: 120px\" summary=\"This figure has two columns. At the top of the figure, the right column contains 5x squared minus 8x plus 4. One row down, the left column says \u201cSubstitute 4 for x.\u201d The right column contains 5 times 4 squared minus 8 times 4 plus 4. One row down, the left column says \u201cSimplify the exponents.\u201d The right column contains 5 times 16 minus 8 times 4 plus 4. One row down, the left column says \u201cMultiply.\u201d The right column contains 80 minus 32 plus 4. One row down, the left column says \u201cSimplify.\u201d The right column contains 52.\" width=\"100%\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 479.358px\">a) \\(x=4\\)<\/td>\r\n<td style=\"width: 622.477px\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 479.358px\"><\/td>\r\n<td style=\"width: 622.477px\">[latex]5 x^2-8 x+4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 479.358px\"><span id=\"eip-id1168741859844\" data-type=\"media\" data-alt=\"Substitute negative 2 for x.\">Substitute [latex]{\\color{red}{4}}[\/latex] for x.<\/span><\/td>\r\n<td style=\"width: 622.477px\">[latex]5({\\color{red}{4}})^2-8({\\color{red}{4}})+4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 479.358px\">Simplify the exponents.<\/td>\r\n<td style=\"width: 622.477px\">\u00a0[latex]5 \\cdot 16-8 \\cdot 4+4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 479.358px\">Multiply.<\/td>\r\n<td style=\"width: 622.477px\">[latex]80-32+4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 479.358px\">Simplify.<\/td>\r\n<td style=\"width: 622.477px\">[latex]52[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168745407360\" class=\"unnumbered unstyled\" style=\"width: 100%\" summary=\"This figure has two columns. At the top of the figure, the right column contains 5x squared minus 8x plus 4. One row down, the left column says \u201cSubstitute negative 2 for x.\u201d The right column contains 5 times negative 2 squared minus 8 times negative 2 plus 4. One row down, the left column says \u201cSimplify the exponents.\u201d The right column contains 5 times 4 minus 8 times negative 2 plus 4. One row down, the left column says \u201cMultiply.\u201d The right column contains 20 plus 16 plus 4. One row down, the left column says \u201cSimplify.\u201d The right column contains 40.\" width=\"100%\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 43.9929%\">b) \\(x=-2\\)<\/td>\r\n<td style=\"width: 55.8304%\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 43.9929%\"><\/td>\r\n<td style=\"width: 55.8304%\">\u00a0[latex]5 x^2-8 x+4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 43.9929%\" data-align=\"left\"><span id=\"eip-id1168741859844\" data-type=\"media\" data-alt=\"Substitute negative 2 for x.\">Substitute [latex]{\\color{red}{-2}}[\/latex] for x .<\/span><\/td>\r\n<td style=\"width: 55.8304%\"><span id=\"eip-id1168741802146\" data-type=\"media\" data-alt=\"5 times negative 2 squared minus 8 times negative 2 plus 4.\">[latex]5({\\color{red}{-2}})^2-8({\\color{red}{-2}})+4[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 43.9929%\">Simplify the exponents.<\/td>\r\n<td style=\"width: 55.8304%\">[latex]5 \\cdot 4 -8 (-2) +4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 43.9929%\">Multiply.<\/td>\r\n<td style=\"width: 55.8304%\">[latex]20+16+4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 43.9929%\">Simplify.<\/td>\r\n<td style=\"width: 55.8304%\">[latex]40[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168744046237\" class=\"unnumbered unstyled\" style=\"width: 100%\" summary=\"This figure has two columns. At the top of the figure, the right column contains 5x squared minus 8x plus 4. One row down, the left column says \u201cSubstitute 0 for x.\u201d The right column contains 5 times 0 squared minus 8 times 0 plus 4. One row down, the left column says \u201cSimplify the exponents.\u201d The right column contains 5 times 0 minus 8 times 0 plus 4. One row down, the left column says \u201cMultiply.\u201d The right column contains 0 plus 0 plus 4. One row down, the left column says \u201cSimplify.\u201d The right column contains 4.\" width=\"100%\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 44.1696%\">c) \\(x=0\\)<\/td>\r\n<td style=\"width: 55.742%\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 44.1696%\"><\/td>\r\n<td style=\"width: 55.742%\">[latex]5 x^2-8 x+4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 44.1696%\" data-align=\"left\">Substitute [latex]{\\color{red}{0}}[\/latex] for x .<\/td>\r\n<td style=\"width: 55.742%\">[latex]5({\\color{red}{0}})^2-8({\\color{red}{0}})+4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 44.1696%\">Simplify the exponents.<\/td>\r\n<td style=\"width: 55.742%\">[latex]5 \\cdot 0-8 \\cdot 0+4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 44.1696%\">Multiply.<\/td>\r\n<td style=\"width: 55.742%\">[latex]0+0+4[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 44.1696%\">Simplify.<\/td>\r\n<td style=\"width: 55.742%\">[latex]4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596396726\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596396730\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596396732\" data-type=\"problem\">\r\n<p id=\"fs-id1169596396734\">Evaluate: \\(3{x}^{2}+2x-15\\) when<\/p>\r\n\r\n<ol id=\"fs-id1168745059161\" class=\"circled\" type=\"a\">\r\n \t<li>\\(x=3\\)<\/li>\r\n \t<li>\\(x=-5\\)<\/li>\r\n \t<li>\\(x=0\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1169596405415\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596405417\">a) \\(18\\) b) \\(50\\) c) \\(-15\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596405445\" data-type=\"problem\">\r\n<p id=\"fs-id1169596405447\">Evaluate: \\(5{z}^{2}-z-4\\) when<\/p>\r\n\r\n<ol id=\"fs-id1168742059174\" class=\"circled\" type=\"a\">\r\n \t<li>\\(z=-2\\)<\/li>\r\n \t<li>\\(z=0\\)<\/li>\r\n \t<li>\\(z=2\\)<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div id=\"fs-id1169596306478\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596306480\">a) \\(18\\) b) \\(-4\\) c) \\(14\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596405439\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596405443\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596306478\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596306506\" data-type=\"problem\">\r\n<p id=\"fs-id1169596306508\">The polynomial \\(-16{t}^{2}+250\\) gives the height of a ball \\(t\\) seconds after it is dropped from a 250 foot tall building. Find the height after \\(t=2\\) seconds.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596361348\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-963\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(-16{t}^{2}+250\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute \\(t=2\\).<\/td>\r\n<td>\\(-16{\\left(2\\right)}^{2}+250\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(-16\\cdot 4+250\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(-64+250\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(186\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>After 2 seconds the height of the ball is 186 feet.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596497369\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596497373\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596497375\" data-type=\"problem\">\r\n<p id=\"fs-id1169596497377\">The polynomial \\(-16{t}^{2}+250\\) gives the height of a ball \\(t\\) seconds after it is dropped from a 250-foot tall building. Find the height after \\(t=0\\) seconds.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596497410\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596497413\">\\(250\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596497428\" data-type=\"problem\">\r\n<p id=\"fs-id1169596497431\">The polynomial \\(-16{t}^{2}+250\\) gives the height of a ball \\(t\\) seconds after it is dropped from a 250-foot tall building. Find the height after \\(t=3\\) seconds.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596369518\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596369520\">\\(106\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596497422\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596497426\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596369518\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596369534\" data-type=\"problem\">\r\n<p id=\"fs-id1169596369536\">The polynomial \\(6{x}^{2}+15xy\\) 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 sides of height <em data-effect=\"italics\">y<\/em> feet. Find the cost of producing a box with \\(x=4\\) feet and \\(y=6\\) feet.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596314860\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1168743983267\" class=\"unnumbered unstyled\" style=\"width: 890px\" summary=\"This figure has two columns. At the top of the figure, the right column contains 6x squared plus 15xy. One row down, the left column says \u201cSubstitute x equals 4, y equals 6\u201d. The right column contains 6 times 4 squared plus 15 times 4 times 6. One row down, the left column says \u201cSimplify.\u201d The right column contains 6 times 16 plus 15 times 4 times 6. One row down, the left column says \u201cSimplify.\u201d The right column contains 96 plus 360. One row down, the left column says \u201cSimplify.\u201d The right column contains 456\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 523.638px\"><\/td>\r\n<td style=\"width: 336.425px\"><span id=\"eip-id1168743983286\" data-type=\"media\" data-alt=\"6 x squared plus 15 x y.\">[latex]6{x}^{2}+15xy[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 523.638px\" data-align=\"left\">Substitute [latex]x=\\color{red}{4}[\/latex] , [latex]y=\\color{blue}{6}[\/latex]<\/td>\r\n<td style=\"width: 336.425px\"><span id=\"eip-id1168746651696\" data-type=\"media\" data-alt=\"6 times 4 squared plus 15 times 4 times 6.\">[latex]6({\\color{red}{4}})^2+15({\\color{red}{4}})({\\color{blue}{6}})[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 523.638px\">Simplify.<\/td>\r\n<td style=\"width: 336.425px\">[latex]6 \\cdot 16 + 15({\\color{red}{4}})({\\color{blue}{6}})[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 523.638px\">Simplify.<\/td>\r\n<td style=\"width: 336.425px\">[latex]96+360[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 523.638px\">Simplify.<\/td>\r\n<td style=\"width: 336.425px\">[latex]456[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 523.638px\"><\/td>\r\n<td style=\"width: 336.425px\">The cost of producing the box is \\$456.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596314885\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1169596314889\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596314891\" data-type=\"problem\">\r\n<p id=\"fs-id1169596314894\">The polynomial \\(6{x}^{2}+15xy\\) 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 sides of height <em data-effect=\"italics\">y<\/em> feet. Find the cost of producing a box with \\(x=6\\) feet and \\(y=4\\) feet.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596365368\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596365370\">\\$576<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1169596365383\" data-type=\"problem\">\r\n<p id=\"fs-id1169596365385\">The polynomial \\(6{x}^{2}+15xy\\) 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 sides of height <em data-effect=\"italics\">y<\/em> feet. Find the cost of producing a box with \\(x=5\\) feet and \\(y=8\\) feet.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1169596365439\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1169596365441\">\\$750<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596374921\" class=\"media-2\" data-type=\"note\">\r\n<p id=\"fs-id1169596374925\">Access these online resources for additional instruction and practice with adding and subtracting polynomials.<\/p>\r\n\r\n<ul id=\"fs-id1169596374929\" data-display=\"block\">\r\n \t<li><a href=\"https:\/\/openstax.org\/l\/25Addsubtrpoly1\">Add and Subtract Polynomials 1<\/a><\/li>\r\n \t<li><a href=\"https:\/\/openstax.org\/l\/25Addsubtrpoly2\">Add and Subtract Polynomials 2<\/a><\/li>\r\n \t<li><a href=\"https:\/\/openstax.org\/l\/25Addsubtrpoly3\">Add and Subtract Polynomial 3<\/a><\/li>\r\n \t<li><a href=\"https:\/\/openstax.org\/l\/25Addsubtrpoly4\">Add and Subtract Polynomial 4<\/a><\/li>\r\n<\/ul>\r\n<\/div>\r\n<h1>Key Concepts<\/h1>\r\n<ul id=\"fs-id1169596374969\" data-bullet-style=\"bullet\">\r\n \t<li><strong data-effect=\"bold\">Monomials<\/strong>\r\n<ul id=\"fs-id1169596374981\" data-bullet-style=\"open-circle\">\r\n \t<li>A monomial is a term of the form \\(a{x}^{m}\\), where \\(a\\) is a constant and \\(m\\) is a whole number<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Polynomials<\/strong>\r\n<ul id=\"fs-id1169596497714\" data-bullet-style=\"open-circle\">\r\n \t<li><strong data-effect=\"bold\">polynomial<\/strong>\u2014A monomial, or two or more monomials combined by addition or subtraction is a polynomial.<\/li>\r\n \t<li><strong data-effect=\"bold\">monomial<\/strong>\u2014A polynomial with exactly one term is called a monomial.<\/li>\r\n \t<li><strong data-effect=\"bold\">binomial<\/strong>\u2014A polynomial with exactly two terms is called a binomial.<\/li>\r\n \t<li><strong data-effect=\"bold\">trinomial<\/strong>\u2014A polynomial with exactly three terms is called a trinomial.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Degree of a Polynomial<\/strong>\r\n<ul id=\"fs-id1171791456751\" data-bullet-style=\"open-circle\">\r\n \t<li>The <strong data-effect=\"bold\">degree of a term<\/strong> is the sum of the exponents of its variables.<\/li>\r\n \t<li>The <strong data-effect=\"bold\">degree of a constant<\/strong> is 0.<\/li>\r\n \t<li>The <strong data-effect=\"bold\">degree of a polynomial<\/strong> is the highest degree of all its terms.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h1>Glossary<\/h1>\r\n<div class=\"textbox shaded\">\r\n<dl id=\"fs-id1169596390906\">\r\n \t<dt>binomial<\/dt>\r\n \t<dd id=\"fs-id1169596390912\">A binomial is a polynomial with exactly two terms.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1169596390916\">\r\n \t<dt>degree of a constant<\/dt>\r\n \t<dd id=\"fs-id1169596390921\">The degree of any constant is 0.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1169596390925\">\r\n \t<dt>degree of a polynomial<\/dt>\r\n \t<dd id=\"fs-id1169596390931\">The degree of a polynomial is the highest degree of all its terms.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1169596390935\">\r\n \t<dt>degree of a term<\/dt>\r\n \t<dd id=\"fs-id1169596390940\">The degree of a term is the exponent of its variable.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1169596390945\">\r\n \t<dt>monomial<\/dt>\r\n \t<dd id=\"fs-id1169596390950\">A monomial is a term of the form \\(a{x}^{m}\\), where \\(a\\) is a constant and \\(m\\) is a whole number; a monomial has exactly one term.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1169596380528\">\r\n \t<dt>polynomial<\/dt>\r\n \t<dd id=\"fs-id1169596380533\">A polynomial is a monomial, or two or more monomials combined by addition or subtraction.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1169596380539\">\r\n \t<dt>standard form<\/dt>\r\n \t<dd id=\"fs-id1169596380544\">A polynomial is in standard form when the terms of a polynomial are written in descending order of degrees.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1169596380549\">\r\n \t<dt>trinomial<\/dt>\r\n \t<dd id=\"fs-id1169596380555\">A trinomial is a polynomial with exactly three terms.<\/dd>\r\n<\/dl>\r\nType your textbox content here.\r\n\r\n<\/div>\r\n<h1>Practice Makes Perfect<\/h1>\r\n<h2 id=\"fs-id1169596367644\" style=\"text-align: left\">Identify Polynomials, Monomials, Binomials, and Trinomials<\/h2>\r\n<p id=\"fs-id1168741892941\">In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1166426192935\">1.<\/p>\r\na) \\(81{b}^{5}-24{b}^{3}+1\\)\r\nb) \\(5{c}^{3}+11{c}^{2}-c-8\\)\r\nc) \\(\\dfrac{14}{15}y+\\dfrac{1}{7}\\)\r\nd) 5\r\ne) \\(4y+17\\)<\/td>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1166425964014\">2.<\/p>\r\na) \\({x}^{2}-{y}^{2}\\)\r\nb) \\(-13{c}^{4}\\)\r\nc) \\({x}^{2}+5x-7\\)\r\nd) \\({x}^{2}{y}^{2}-2xy+8\\)\r\ne) 19<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1166426185366\">3.<\/p>\r\na) \\(8-3x\\)\r\nb) \\({z}^{2}-5z-6\\)\r\nc) \\({y}^{3}-8{y}^{2}+2y-16\\)\r\nd) \\(81{b}^{5}-24{b}^{3}+1\\)\r\ne) \\(-18\\)<\/td>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1166426272537\">4.<\/p>\r\na) \\(11{y}^{2}\\)\r\nb) \\(-73\\)\r\nc) \\(6{x}^{2}-3xy+4x-2y+{y}^{2}\\)\r\nd) \\(4y+17\\)\r\ne) \\(5{c}^{3}+11{c}^{2}-c-8\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 id=\"fs-id1169596499577\" style=\"text-align: left\"><strong data-effect=\"bold\">\r\n<\/strong>Determine the Degree of Polynomials<\/h2>\r\n<p id=\"fs-id1168741855043\">In the following exercises, determine the degree of each polynomial.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%;height: 266px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 140px\">\r\n<td style=\"width: 50%;height: 140px\">\r\n<p id=\"fs-id1166425926085\">5.<\/p>\r\na) \\(6{a}^{2}+12a+14\\)\r\nb) \\(18x{y}^{2}z\\)\r\nc) \\(5x+2\\)\r\nd) \\({y}^{3}-8{y}^{2}+2y-16\\)\r\ne) \\(-24\\)<\/td>\r\n<td style=\"width: 50%;height: 140px\">\r\n<p id=\"fs-id1166426253457\">6.<\/p>\r\na) \\(9{y}^{3}-10{y}^{2}+2y-6\\)\r\nb) \\(-12{p}^{4}\\)\r\nc) \\({a}^{2}+9a+18\\)\r\nd) \\(20{x}^{2}{y}^{2}-10{a}^{2}{b}^{2}+30\\)\r\ne) 17<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">\r\n<p id=\"fs-id1166425935275\">7.<\/p>\r\na) \\(14-29x\\)\r\nb) \\({z}^{2}-5z-6\\)\r\nc) \\({y}^{3}-8{y}^{2}+2y-16\\)\r\nd) \\(23a{b}^{2}-14\\)\r\ne) \\(-3\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">\r\n<p id=\"fs-id1166425972094\">8.<\/p>\r\na) \\(62{y}^{2}\\)\r\nb) 15\r\nc) \\(6{x}^{2}-3xy+4x-2y+{y}^{2}\\)\r\nd) \\(10-9x\\)\r\ne) \\({m}^{4}+4{m}^{3}+6{m}^{2}+4m+1\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 id=\"fs-id1169596372469\" style=\"text-align: left\"><strong data-effect=\"bold\">\r\n<\/strong>Add and Subtract Monomials<\/h2>\r\n<p id=\"fs-id1168745505449\">In the following exercises, add or subtract the monomials.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%;height: 140px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">9. \\({7x}^{2}+5{x}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">10. \\({4y}^{3}+6{y}^{3}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">11. \\(-12w+18w\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">12. \\(-3m+9m\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">13. \\(\\text{4a}-9a\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">14. \\(-y-5y\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">15. \\(28x-\\left(-12x\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">16. \\(13z-\\left(-4z\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">17. \\(-5b-17b\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">18. \\(-10x-35x\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">19. \\(12a+5b-22a\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">20. \\(\\text{14x}-3y-13x\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">21. \\(2{a}^{2}+{b}^{2}-6{a}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">22. \\(5{u}^{2}+4{v}^{2}-6{u}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">23. \\(x{y}^{2}-5x-5{y}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">24. \\(p{q}^{2}-4p-3{q}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">25. \\({a}^{2}b-4a-5a{b}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">26. \\({x}^{2}y-3x+7x{y}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">27. \\(\\text{12a}+8b\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">28. \\(\\text{19y}+5z\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">29. Add: \\(4a,-3b,-8a\\)<\/td>\r\n<td style=\"width: 50%\">30. Add: \\(4x,3y,-3x\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">31. Subtract \\(5{x}^{6}\\text{from}-12{x}^{6}\\).<\/td>\r\n<td style=\"width: 50%\">32. Subtract \\(2{p}^{4}\\text{from}-7{p}^{4}\\).<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 id=\"fs-id1169596402107\" style=\"text-align: left\">Add and Subtract Polynomials<\/h2>\r\n<p id=\"fs-id1168742190618\">In the following exercises, add or subtract the polynomials.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">33. \\(\\left(5{y}^{2}+12y+4\\right)+\\left(6{y}^{2}-8y+7\\right)\\)<\/td>\r\n<td style=\"width: 50%\">34. \\(\\left(4{y}^{2}+10y+3\\right)+\\left(8{y}^{2}-6y+5\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">35. \\(\\left({x}^{2}+6x+8\\right)+\\left(-4{x}^{2}+11x-9\\right)\\)<\/td>\r\n<td style=\"width: 50%\">36. \\(\\left({y}^{2}+9y+4\\right)+\\left(-2{y}^{2}-5y-1\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">37. \\(\\left(8{x}^{2}-5x+2\\right)+\\left(3{x}^{2}+3\\right)\\)<\/td>\r\n<td style=\"width: 50%\">38. \\(\\left(7{x}^{2}-9x+2\\right)+\\left(6{x}^{2}-4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">39. \\(\\left(5{a}^{2}+8\\right)+\\left({a}^{2}-4a-9\\right)\\)<\/td>\r\n<td style=\"width: 50%\">40. \\(\\left({p}^{2}-6p-18\\right)+\\left(2{p}^{2}+11\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">41. \\(\\left(4{m}^{2}-6m-3\\right)-\\left(2{m}^{2}+m-7\\right)\\)<\/td>\r\n<td style=\"width: 50%\">42. \\(\\left(3{b}^{2}-4b+1\\right)-\\left(5{b}^{2}-b-2\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">43. \\(\\left({a}^{2}+8a+5\\right)-\\left({a}^{2}-3a+2\\right)\\)<\/td>\r\n<td style=\"width: 50%\">44. \\(\\left({b}^{2}-7b+5\\right)-\\left({b}^{2}-2b+9\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">45. \\(\\left(12{s}^{2}-15s\\right)-\\left(s-9\\right)\\)<\/td>\r\n<td style=\"width: 50%\">46. \\(\\left(10{r}^{2}-20r\\right)-\\left(r-8\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">47. Subtract \\(\\left(9{x}^{2}+2\\right)\\) from \\(\\left(12{x}^{2}-x+6\\right)\\).<\/td>\r\n<td style=\"width: 50%\">48. Subtract \\(\\left(5{y}^{2}-y+12\\right)\\) from \\(\\left(10{y}^{2}-8y-20\\right)\\).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">49. Subtract \\(\\left(7{w}^{2}-4w+2\\right)\\) from \\(\\left(8{w}^{2}-w+6\\right)\\).<\/td>\r\n<td style=\"width: 50%\">50. Subtract \\(\\left(5{x}^{2}-x+12\\right)\\) from \\(\\left(9{x}^{2}-6x-20\\right)\\).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">51. Find the sum of \\(\\left(2{p}^{3}-8\\right)\\) and \\(\\left({p}^{2}+9p+18\\right)\\).<\/td>\r\n<td style=\"width: 50%\">52. Find the sum of \\(\\left({q}^{2}+4q+13\\right)\\) and \\(\\left(7{q}^{3}-3\\right)\\).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">53. Find the sum of \\(\\left(8{a}^{3}-8a\\right)\\) and \\(\\left({a}^{2}+6a+12\\right)\\).<\/td>\r\n<td style=\"width: 50%\">54. Find the sum of \\(\\left({b}^{2}+5b+13\\right)\\) and \\(\\left(4{b}^{3}-6\\right)\\).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">55. Find the difference of\r\n\\(\\left({w}^{2}+w-42\\right)\\) and\r\n\\(\\left({w}^{2}-10w+24\\right)\\).<\/td>\r\n<td style=\"width: 50%\">56. Find the difference of\r\n\\(\\left({z}^{2}-3z-18\\right)\\) and\r\n\\(\\left({z}^{2}+5z-20\\right)\\).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">57. Find the difference of\r\n\\(\\left({c}^{2}+4c-33\\right)\\) and\r\n\\(\\left({c}^{2}-8c+12\\right)\\).<\/td>\r\n<td style=\"width: 50%\">58. Find the difference of\r\n\\(\\left({t}^{2}-5t-15\\right)\\) and\r\n\\(\\left({t}^{2}+4t-17\\right)\\).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">59. \\(\\left(7{x}^{2}-2xy+6{y}^{2}\\right)+\\left(3{x}^{2}-5xy\\right)\\)<\/td>\r\n<td style=\"width: 50%\">60. \\(\\left(-5{x}^{2}-4xy-3{y}^{2}\\right)+\\left(2{x}^{2}-7xy\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">61. \\(\\left(7{m}^{2}+mn-8{n}^{2}\\right)+\\left(3{m}^{2}+2mn\\right)\\)<\/td>\r\n<td style=\"width: 50%\">62. \\(\\left(2{r}^{2}-3rs-2{s}^{2}\\right)+\\left(5{r}^{2}-3rs\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">63. \\(\\left({a}^{2}-{b}^{2}\\right)-\\left({a}^{2}+3ab-4{b}^{2}\\right)\\)<\/td>\r\n<td style=\"width: 50%\">64. \\(\\left({m}^{2}+2{n}^{2}\\right)-\\left({m}^{2}-8mn-{n}^{2}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">65. \\(\\left({u}^{2}-{v}^{2}\\right)-\\left({u}^{2}-4uv-3{v}^{2}\\right)\\)<\/td>\r\n<td style=\"width: 50%\">66. \\(\\left({j}^{2}-{k}^{2}\\right)-\\left({j}^{2}-8jk-5{k}^{2}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">67. \\(\\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)\\)<\/td>\r\n<td style=\"width: 50%\">68. \\(\\left({a}^{3}-2{a}^{2}b\\right)+\\left(a{b}^{2}+{b}^{3}\\right)\\)\\(-\\left(3{a}^{2}b+4a{b}^{2}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">69. \\(\\left({x}^{3}-{x}^{2}y\\right)-\\left(4x{y}^{2}-{y}^{3}\\right)\\)\\(+\\left(3{x}^{2}y-x{y}^{2}\\right)\\)<\/td>\r\n<td style=\"width: 50%\">70. \\(\\left({x}^{3}-2{x}^{2}y\\right)-\\left(x{y}^{2}-3{y}^{3}\\right)\\)\\(-\\left({x}^{2}y-4x{y}^{2}\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 id=\"fs-id1169596411950\" style=\"text-align: left\">Evaluate a Polynomial for a Given Value<\/h2>\r\n<p id=\"fs-id1168742058387\">In the following exercises, evaluate each polynomial for the given value.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%;height: 235px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 123px\">\r\n<td style=\"width: 50%;height: 123px\">\r\n<div id=\"fs-id1169596411958\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596411960\" data-type=\"problem\">\r\n<p id=\"fs-id1169596411962\">71. Evaluate \\(8{y}^{2}-3y+2\\) when:<\/p>\r\n<p id=\"fs-id1166423871629\">a) \\(y=5\\)\r\nb) \\(y=-2\\)\r\nc) \\(y=0\\)<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596455663\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596455665\" data-type=\"problem\">\r\n<p id=\"fs-id1169596455667\"><\/p>\r\n\r\n<\/div>\r\n<\/div><\/td>\r\n<td style=\"width: 50%;height: 123px\">\r\n<div id=\"fs-id1169596455663\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596455665\" data-type=\"problem\">\r\n<p id=\"fs-id1169596455667\">72. Evaluate \\(5{y}^{2}-y-7\\) when:<\/p>\r\n<p id=\"fs-id1166425960377\">a) \\(y=-4\\)\r\nb) \\(y=1\\)\r\nc) \\(y=0\\)<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1169596455733\" data-type=\"exercise\">\r\n<div id=\"fs-id1169596455736\" data-type=\"problem\">\r\n<p id=\"fs-id1169596455738\"><\/p>\r\n\r\n<\/div>\r\n<\/div><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">\r\n<p id=\"fs-id1169596455738\">73. Evaluate \\(4-36x\\) when:<\/p>\r\n<p id=\"fs-id1166423760338\">a) \\(x=3\\)\r\nb) \\(x=0\\)\r\nc) \\(x=-1\\)<\/p>\r\n<\/td>\r\n<td style=\"width: 50%;height: 14px\">\r\n<p id=\"fs-id1169596455802\">74. Evaluate \\(16-36{x}^{2}\\) when:<\/p>\r\n<p id=\"fs-id1166426184684\">a) \\(x=-1\\)\r\nb) \\(x=0\\)\r\nc) \\(x=2\\)<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">75. A painter drops a brush from a platform 75 feet high. The polynomial \\(-16{t}^{2}+75\\) gives the height of the brush \\(t\\) seconds after it was dropped. Find the height after \\(t=2\\) seconds.<\/td>\r\n<td style=\"width: 50%;height: 14px\">76. A girl drops a ball off a cliff into the ocean. The polynomial \\(-16{t}^{2}+250\\) gives the height of a ball \\(t\\) seconds after it is dropped from a 250-foot tall cliff. Find the height after \\(t=2\\) seconds.<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">77. 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 \\(-4{p}^{2}+420p\\). Find the revenue received when \\(p=60\\) dollars.<\/td>\r\n<td style=\"width: 50%;height: 14px\">78. 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 \\(-4{p}^{2}+420p\\). Find the revenue received when \\(p=90\\) dollars.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 data-type=\"title\">Everyday Math<\/h2>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">79. <strong data-effect=\"bold\">Fuel Efficiency<\/strong> The fuel efficiency (in miles per gallon) of a car going at a speed of \\(x\\) miles per hour is given by the polynomial \\(-\\dfrac{1}{150}{x}^{2}+\\dfrac{1}{3}x\\). Find the fuel efficiency when \\(x=30 \\text{mph}\\).<\/td>\r\n<td style=\"width: 50%\">80.<strong data-effect=\"bold\"> Stopping Distance<\/strong> The number of feet it takes for a car traveling at \\(x\\) miles per hour to stop on dry, level concrete is given by the polynomial \\(0.06{x}^{2}+1.1x\\). Find the stopping distance when \\(x=40\\text{mph}\\).<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">81.<strong data-effect=\"bold\"> Rental Cost<\/strong> The cost to rent a rug cleaner for \\(d\\) days is given by the polynomial \\(5.50d+25\\). Find the cost to rent the cleaner for 6 days.<\/td>\r\n<td style=\"width: 50%\">82.<strong data-effect=\"bold\"> Height of Projectile<\/strong> The height (in feet) of an object projected upward is given by the polynomial \\(-16{t}^{2}+60t+90\\) where \\(t\\) represents time in seconds. Find the height after \\(t=2.5\\) seconds.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">83.<strong data-effect=\"bold\"> Temperature Conversion<\/strong> The temperature in degrees Fahrenheit is given by the polynomial \\(\\dfrac{9}{5}c+32\\) where \\(c\\) represents the temperature in degrees Celsius. Find the temperature in degrees Fahrenheit when \\(c=65\\)\u00b0.<\/td>\r\n<td style=\"width: 50%\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2 data-type=\"title\">Writing Exercises<\/h2>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">84. Using your own words, explain the difference between a monomial, a binomial, and a trinomial.<\/td>\r\n<td style=\"width: 50%\">85. Using your own words, explain the difference between a polynomial with five terms and a polynomial with a degree of 5.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">86. Ariana thinks the sum \\(6{y}^{2}+5{y}^{4}\\) is \\(11{y}^{6}\\). What is wrong with her reasoning?<\/td>\r\n<td style=\"width: 50%\">87. Jonathan thinks that \\(\\dfrac{1}{3}\\) and \\(\\dfrac{1}{x}\\) are both monomials. What is wrong with his reasoning?<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Answers<\/h1>\r\n<table style=\"border-collapse: collapse;width: 100%;height: 371px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 34px\">\r\n<td style=\"width: 50%;height: 34px\">1. a) trinomial b) polynomial c) binomial d) monomial e) binomial<\/td>\r\n<td style=\"width: 50%;height: 34px\">3. a) binomial b) trinomial c) polynomial d) trinomial e) monomial<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">5. a) 2 b) 4 c) 1 d) 3 e) 0<\/td>\r\n<td style=\"width: 50%;height: 16px\">7. a) 1 b) 2 c) 3 d) 3 e) 0<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">9. \\(12{x}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">11. \\(6w\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">13. \\(-5a\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">15. \\(40x\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">17. \\(-22b\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">19. \\(-10a+5b\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">21. \\(-4{a}^{2}+{b}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">23. \\(x{y}^{2}-5x-5{y}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">25. \\({a}^{2}b-4a-5a{b}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">27. \\(\\text{12a}+8b\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">29. \\(-4a-3b\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">31. \\(-17{x}^{6}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">33. \\(11{y}^{2}+4y+11\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">35. \\(-3{x}^{2}+17x-1\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">37. \\(11{x}^{2}-5x+5\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">39. \\(6{a}^{2}-4a-1\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">41. \\(2{m}^{2}-7m+4\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">43. \\(11a+3\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px\">\r\n<td style=\"width: 50%;height: 17px\">45. \\(12{s}^{2}-16s+9\\)<\/td>\r\n<td style=\"width: 50%;height: 17px\">47. \\(3{x}^{2}-x+4\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">49. \\({w}^{2}+3w+4\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">51. \\(2{p}^{3}+{p}^{2}+9p+10\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">53. \\(8{a}^{3}+{a}^{2}-2a+12\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">55. \\(11w-64\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">57. \\(12c-45\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">59. \\(10{x}^{2}-7xy+6{y}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">61. \\(10{m}^{2}+3mn-8{n}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">63. \\(-3ab+3{b}^{2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">65. \\(4uv+2{v}^{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">67. \\({p}^{3}-6{p}^{2}q+p{q}^{2}+4{q}^{3}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">69. \\({x}^{3}+2{x}^{2}y-5x{y}^{2}+{y}^{3}\\)<\/td>\r\n<td style=\"width: 50%;height: 16px\">71. a) 187 b) 40 c) 2<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">73. a) \u2212104 b) 4 c) 40<\/td>\r\n<td style=\"width: 50%;height: 16px\">75. 11<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">77. \\$10,800<\/td>\r\n<td style=\"width: 50%;height: 16px\">79. 4 miles per gallon<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">81. \\$58<\/td>\r\n<td style=\"width: 50%;height: 16px\">83. 149<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 50%;height: 16px\">85. Answers will vary.<\/td>\r\n<td style=\"width: 50%;height: 16px\">87. Answers will vary.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Attributions<\/h1>\r\nThis chapter has been adapted from \u201cAdd and Subtract Polynomials\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.\r\n\r\n<!-- pb_fixme -->","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Identify polynomials, monomials, binomials, and trinomials<\/li>\n<li>Determine the degree of polynomials<\/li>\n<li>Add and subtract monomials<\/li>\n<li>Add and subtract polynomials<\/li>\n<li>Evaluate a polynomial for a given value<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Identify Polynomials, Monomials, Binomials and Trinomials<\/h1>\n<p id=\"fs-id1169596310635\">You have learned that a <em data-effect=\"italics\">term<\/em> is a constant or the product of a constant and one or more variables. When it is of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b1f34ffb1b277daca10222d739f07a74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#123;&#120;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_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;\" \/> is a constant and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e2ab2eed1ecd297014b27aaa529e23c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> is a whole number, it is called a monomial. Some examples of monomial are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-94c41ec7f54b13f43e01ebee7c7cbaa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#44;&#45;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#52;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"90\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dcf293dc43caba8a9253750c48ed4a12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#123;&#122;&#125;&#94;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"33\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div id=\"fs-id1169596365842\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Monomials<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A monomial is a term of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b1f34ffb1b277daca10222d739f07a74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#123;&#120;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_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;\" \/> is a constant and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e2ab2eed1ecd297014b27aaa529e23c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> is a positive whole number.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596286467\">A monomial, or two or more monomials combined by addition or subtraction, is a polynomial. 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 trinomial has exactly three terms. There are no special names for polynomials with more than three terms.<\/p>\n<div id=\"fs-id1169596312244\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Polynomials<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1168745072439\">polynomial\u2014A monomial, or two or more monomials combined by addition or subtraction, is a polynomial.<\/p>\n<ul id=\"fs-id1169596372377\" data-bullet-style=\"open-circle\">\n<li><strong data-effect=\"bold\">monomial<\/strong>\u2014A polynomial with exactly one term is called a monomial.<\/li>\n<li><strong>binomial<\/strong>\u2014A polynomial with exactly two terms is called a binomial.<\/li>\n<li><strong>trinomial<\/strong>\u2014A polynomial with exactly three terms is called a trinomial.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596360597\">Here are some examples of polynomials.<\/p>\n<p id=\"fs-id1169596286034\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a3881081551e5b64ea29ee2bd5790ec1_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;&#108;&#108;&#108;&#108;&#108;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#111;&#108;&#121;&#110;&#111;&#109;&#105;&#97;&#108;&#125;&#32;&#38;&#32;&#98;&#43;&#49;&#32;&#38;&#32;&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#121;&#43;&#50;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#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;&#38;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#111;&#110;&#111;&#109;&#105;&#97;&#108;&#125;&#38;&#32;&#49;&#52;&#38;&#32;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#32;&#38;&#32;&#45;&#57;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#32;&#38;&#32;&#45;&#49;&#51;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#105;&#110;&#111;&#109;&#105;&#97;&#108;&#125;&#32;&#38;&#97;&#43;&#55;&#38;&#32;&#52;&#98;&#45;&#53;&#32;&#38;&#32;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#54;&#32;&#38;&#32;&#51;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#114;&#105;&#110;&#111;&#109;&#105;&#97;&#108;&#125;&#32;&#38;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#120;&#43;&#49;&#50;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#57;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#121;&#45;&#56;&#32;&#92;&#113;&#113;&#117;&#97;&#100;&#32;&#38;&#32;&#54;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#45;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#43;&#56;&#109;&#32;&#38;&#32;&#123;&#122;&#125;&#94;&#123;&#52;&#125;&#43;&#51;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#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=\"625\" style=\"vertical-align: -37px;\" \/><\/p>\n<p id=\"fs-id1169596281141\">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<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596499092\" data-type=\"problem\">\n<p id=\"fs-id1169596254275\">Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial.<\/p>\n<ol id=\"fs-id1168745110296\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-09d029b16da8e1d2a94c2d851cfc296d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#121;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1f8f90b973f4ed66ab63e921598723c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-464269a28a7782a76f0047515c6d7b32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#45;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"195\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a68ad887d8448f6fa9f62a12f00b34fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#45;&#53;&#123;&#109;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"70\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-99fb3457364d0aceedf4dc77cb7ee815_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1169596386484\" data-type=\"solution\">\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-163\" class=\"grid\" summary=\"\/\">\n<tbody>\n<tr>\n<td><\/td>\n<td><strong>Polynomial<\/strong><\/td>\n<td><strong>Number of terms<\/strong><\/td>\n<td><strong>Type<\/strong><\/td>\n<\/tr>\n<tr>\n<td>a)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-09d029b16da8e1d2a94c2d851cfc296d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#121;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4cf5983200020861d6bb094a2f1bf0ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>Trinomial<\/td>\n<\/tr>\n<tr>\n<td>b)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1f8f90b973f4ed66ab63e921598723c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#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><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-720df129611fa0a5878be88711a6fb8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"7\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>Monomial<\/td>\n<\/tr>\n<tr>\n<td>c)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-464269a28a7782a76f0047515c6d7b32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#45;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"195\" style=\"vertical-align: -2px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5cd9c99dec32470db3b8d8bbe292cb8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>Polynomial<\/td>\n<\/tr>\n<tr>\n<td>d)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a68ad887d8448f6fa9f62a12f00b34fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#45;&#53;&#123;&#109;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"70\" style=\"vertical-align: 0px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8c6633954227aa72b608b60e92fe0c7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>Binomial<\/td>\n<\/tr>\n<tr>\n<td>e)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-99fb3457364d0aceedf4dc77cb7ee815_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-720df129611fa0a5878be88711a6fb8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"7\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>Monomial<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596404492\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596319079\" data-type=\"exercise\">\n<div id=\"fs-id1169596319081\" data-type=\"problem\">\n<p id=\"fs-id1169596319083\">Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial:<\/p>\n<p id=\"fs-id1168745401854\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d18bfb44731ce1eb598f22c6db47d016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3058386c5f6e20cce8056ea9d0076b4d_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;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ef1bc3cd52303e1a62441f17d637d384_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"111\" style=\"vertical-align: -2px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-22024fb593ff9aa5b3f68344632652a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;&#45;&#52;&#123;&#97;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"64\" style=\"vertical-align: 0px;\" \/>e)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-689b258ef277b1e51a65950768d9a88d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#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 id=\"fs-id1169596497627\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596497629\">a) monomial b) polynomial c) trinomial d) binomial e) monomial<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596399868\" data-type=\"problem\">\n<p id=\"fs-id1169596399870\">Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial:<\/p>\n<p id=\"fs-id1168745201798\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c57f3f98e5997b2df494c0a85fe2bb9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#123;&#122;&#125;&#94;&#123;&#51;&#125;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"65\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-63ba774afe3a5065821323231622e69a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#45;&#53;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"139\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a0e6d2b1ea0c603773133e95113f0093_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"9\" style=\"vertical-align: -12px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-351a2c40452147d5ddd68fd608d3a3d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#45;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#120;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"145\" style=\"vertical-align: 0px;\" \/> e) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0b23c4d04804ce6b5215dddf8f1c6000_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#110;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1169596369494\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596369496\">a) binomial b) trinomial c) monomial d) polynomial e) monomial<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Determine the Degree of Polynomials<\/h1>\n<p id=\"fs-id1169596369612\">The degree of a polynomial and the degree of its terms are determined by the exponents of the variable.<\/p>\n<p id=\"fs-id1169596369616\">A <span class=\"no-emphasis\" data-type=\"term\">monomial<\/span> that has no variable, just a constant, is a special case. The degree of a constant is 0\u2014it has no variable.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Degree of a Polynomial<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169596369626\">The degree of a term is the sum of the exponents of its variables.<\/p>\n<p id=\"fs-id1169596373156\">The degree of a constant is 0.<\/p>\n<p id=\"fs-id1169596373162\">The degree of a polynomial is the highest degree of all its terms.<\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596373170\">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><span id=\"fs-id1169596498644\" data-type=\"media\" data-alt=\"This table has 11 rows and 5 columns. The first column is a header column, and it names each row. The first row is named \u201cMonomial,\u201d and each cell in this row contains a different monomial. The second row is named \u201cDegree,\u201d and each cell in this row contains the degree of the monomial above it. The degree of 14 is 0, the degree of 8y squared is 2, the degree of negative 9x cubed y to the fifth power is 8, and the degree of negative 13a is 1. The third row is named \u201cBinomial,\u201d and each cell in this row contains a different binomial. The fourth row is named \u201cDegree of each term,\u201d and each cell contains the degrees of the two terms in the binomial above it. The fifth row is named \u201cDegree of polynomial,\u201d and each cell contains the degree of the binomial as a whole.\u201d The degrees of the terms in a plus 7 are 0 and 1, and the degree of the whole binomial is 1. The degrees of the terms in 4b squared minus 5b are 2 and 1, and the degree of the whole binomial is 2. The degrees of the terms in x squared y squared minus 16 are 4 and 0, and the degree of the whole binomial is 4. The degrees of the terms in 3n cubed minus 9n squared are 3 and 2, and the degree of the whole binomial is 3. The sixth row is named \u201cTrinomial,\u201d and each cell in this row contains a different trinomial. The seventh row is named \u201cDegree of each term,\u201d and each cell contains the degrees of the three terms in the trinomial above it. The eighth row is named \u201cDegree of polynomial,\u201d and each cell contains the degree of the trinomial as a whole. The degrees of the terms in x squared minus 7x plus 12 are 2, 1, and 0, and the degree of the whole trinomial is 2. The degrees of the terms in 9a squared plus 6ab plus b squared are 2, 2, and 2, and the degree of the trinomial as a whole is 2. The degrees of the terms in 6m to the fourth power minus m cubed n squared plus 8mn to the fifth power are 4, 5, and 6, and the degree of the whole trinomial is 6. The degrees of the terms in z to the fourth power plus 3z squared minus 1 are 4, 2, and 0, and the degree of the whole trinomial is 4. The ninth row is named \u201cPolynomial,\u201d and each cell contains a different polynomial. The tenth row is named \u201cDegree of each term,\u201d and the eleventh row is named \u201cDegree of polynomial.\u201d The degrees of the terms in b plus 1 are 1 and 0, and the degree of the whole polynomial is 1. The degrees of the terms in 4y squared minus 7y plus 2 are 2, 1, and 0, and the degree of the whole polynomial is 2. The degrees of the terms in 4x to the fourth power plus x cubed plus 8x squared minus 9x plus 1 are 4, 3, 2, 1, and 0, and the degree of the whole polynomial is 4.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/uploads\/sites\/1441\/2021\/05\/CNX_ElemAlg_Figure_06_01_001_img_new.jpg\" alt=\"This table has 11 rows and 5 columns. The first column is a header column, and it names each row. The first row is named \u201cMonomial,\u201d and each cell in this row contains a different monomial. The second row is named \u201cDegree,\u201d and each cell in this row contains the degree of the monomial above it. The degree of 14 is 0, the degree of 8y squared is 2, the degree of negative 9x cubed y to the fifth power is 8, and the degree of negative 13a is 1. The third row is named \u201cBinomial,\u201d and each cell in this row contains a different binomial. The fourth row is named \u201cDegree of each term,\u201d and each cell contains the degrees of the two terms in the binomial above it. The fifth row is named \u201cDegree of polynomial,\u201d and each cell contains the degree of the binomial as a whole.\u201d The degrees of the terms in a plus 7 are 0 and 1, and the degree of the whole binomial is 1. The degrees of the terms in 4b squared minus 5b are 2 and 1, and the degree of the whole binomial is 2. The degrees of the terms in x squared y squared minus 16 are 4 and 0, and the degree of the whole binomial is 4. The degrees of the terms in 3n cubed minus 9n squared are 3 and 2, and the degree of the whole binomial is 3. The sixth row is named \u201cTrinomial,\u201d and each cell in this row contains a different trinomial. The seventh row is named \u201cDegree of each term,\u201d and each cell contains the degrees of the three terms in the trinomial above it. The eighth row is named \u201cDegree of polynomial,\u201d and each cell contains the degree of the trinomial as a whole. The degrees of the terms in x squared minus 7x plus 12 are 2, 1, and 0, and the degree of the whole trinomial is 2. The degrees of the terms in 9a squared plus 6ab plus b squared are 2, 2, and 2, and the degree of the trinomial as a whole is 2. The degrees of the terms in 6m to the fourth power minus m cubed n squared plus 8mn to the fifth power are 4, 5, and 6, and the degree of the whole trinomial is 6. The degrees of the terms in z to the fourth power plus 3z squared minus 1 are 4, 2, and 0, and the degree of the whole trinomial is 4. The ninth row is named \u201cPolynomial,\u201d and each cell contains a different polynomial. The tenth row is named \u201cDegree of each term,\u201d and the eleventh row is named \u201cDegree of polynomial.\u201d The degrees of the terms in b plus 1 are 1 and 0, and the degree of the whole polynomial is 1. The degrees of the terms in 4y squared minus 7y plus 2 are 2, 1, and 0, and the degree of the whole polynomial is 2. The degrees of the terms in 4x to the fourth power plus x cubed plus 8x squared minus 9x plus 1 are 4, 3, 2, 1, and 0, and the degree of the whole polynomial is 4.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1169596498652\">A polynomial is in standard form when the terms of a polynomial are written in descending order of degrees. Get in the habit of writing the term with the highest degree first.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596396659\" data-type=\"problem\">\n<p id=\"fs-id1169596396661\">Find the degree of the following polynomials.<\/p>\n<ol id=\"fs-id1168745374893\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e58f8c47d8cab918a651720bb3080529_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"26\" style=\"vertical-align: -4px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-50a60fc4194820e9498bacf96f5b361b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#55;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"97\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-28baf4b08f4375fe370d40fd129e97fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2190d6708f3db5002190ae33372008eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#98;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -2px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5c4db56950fa41a9a5891f4515c7ffe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -4px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1169596374685\" data-type=\"solution\">\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-712\" class=\"grid\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<br \/>\nThe exponent of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-15f1a95c39a36eda2e95d509a5f0f8b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\" \/> is one. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0598b447f85c5b46d7e954bb1dcc11b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#123;&#121;&#125;&#94;&#123;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"48\" style=\"vertical-align: -4px;\" \/><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e58f8c47d8cab918a651720bb3080529_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"26\" style=\"vertical-align: -4px;\" \/><br \/>\nThe degree is 1.<\/td>\n<\/tr>\n<tr>\n<td>b)<br \/>\nThe highest degree of all the terms is 3.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-50a60fc4194820e9498bacf96f5b361b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#55;&#120;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"97\" style=\"vertical-align: -2px;\" \/><br \/>\nThe degree is 3.<\/td>\n<\/tr>\n<tr>\n<td>c)<br \/>\nThe degree of a constant is 0.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-28baf4b08f4375fe370d40fd129e97fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/><br \/>\nThe degree is 0.<\/td>\n<\/tr>\n<tr>\n<td>d)<br \/>\nThe highest degree of all the terms is 2.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2190d6708f3db5002190ae33372008eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#98;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"105\" style=\"vertical-align: -2px;\" \/><br \/>\nThe degree is 2.<\/td>\n<\/tr>\n<tr>\n<td>e)<br \/>\nThe highest degree of all the terms is 3.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5c4db56950fa41a9a5891f4515c7ffe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -4px;\" \/><br \/>\nThe degree is 3.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596500767\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596500770\" data-type=\"exercise\">\n<div id=\"fs-id1169596500772\" data-type=\"problem\">\n<p id=\"fs-id1169596500774\">Find the degree of the following polynomials:<\/p>\n<p id=\"fs-id1168742186774\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cbd70c27f7e58ec8ddba9da38afd9753_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"39\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2d0ee3b8d018fd1503cc435b26b4cee6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#122;&#125;&#94;&#123;&#52;&#125;&#43;&#52;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"110\" style=\"vertical-align: -2px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5e503116d27235708d4d07dc996676dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#99;&#125;&#94;&#123;&#53;&#125;&#123;&#100;&#125;&#94;&#123;&#52;&#125;&#43;&#57;&#123;&#99;&#125;&#94;&#123;&#51;&#125;&#123;&#100;&#125;&#94;&#123;&#57;&#125;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"142\" style=\"vertical-align: -2px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-db1215b0b95d4423df0747547dc54294_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#45;&#52;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -4px;\" \/>e)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-68ac888b00edd47ce83018453d555767_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1169596316182\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596316184\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-720df129611fa0a5878be88711a6fb8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"7\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f1f9e2ad05c194d396ef07691cc5fdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fa0d0abda01a7c5cb5cbbd11df55607a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\" \/> d) 3 e) 0<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596372752\" data-type=\"problem\">\n<p id=\"fs-id1169596372754\">Find the degree of the following polynomials:<\/p>\n<p id=\"fs-id1168742143930\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-043673978ce863b6cd419eb4b7a44afa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b474fecc72bbed1676d90979ea8691fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#98;&#45;&#49;&#55;&#123;&#97;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"80\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5b081e36247ba2d7ac0b442e180cb164_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#43;&#54;&#121;&#43;&#50;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"99\" style=\"vertical-align: -4px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2923d37669a94a6e74f889c21d3ee06f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\" \/>e)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e5c71cec3a475ba9b7368b06af9a7bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#123;&#97;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"29\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1169596396979\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596396981\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-da3c0afc7ce1bb401c977e5c745a16db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5cd9c99dec32470db3b8d8bbe292cb8d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-720df129611fa0a5878be88711a6fb8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"7\" style=\"vertical-align: 0px;\" \/> d) 2 e) 3<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Add and Subtract Monomials<\/h1>\n<p id=\"fs-id1169596396811\">You 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 coefficient.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596396821\" data-type=\"problem\">\n<p id=\"fs-id1169596396824\">Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fc98a7315f24418af1d079e7f41671bb_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;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596370510\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-960\" summary=\"\/\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fc98a7315f24418af1d079e7f41671bb_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;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-06b5f2ab8131a76ee9e9c907478e2e95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#48;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596258575\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596258578\" data-type=\"exercise\">\n<div id=\"fs-id1169596258581\" data-type=\"problem\">\n<p id=\"fs-id1169596258583\">Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9ed76d601fa12a75831b5a9226745835_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;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596497124\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596497126\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5b84297289d82717794c716f52a603b5_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;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596497146\" data-type=\"problem\">\n<p id=\"fs-id1169596497148\">Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-44e5ef9060bc077c5c31ed9835626eb4_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;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596401651\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596401653\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3621f5011b241d9c8b3fa5da269f2189_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;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596497141\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596497144\" data-type=\"exercise\">\n<div id=\"fs-id1169596401651\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596499322\" data-type=\"problem\">\n<p id=\"fs-id1169596499325\">Subtract: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-131e1a2ba1c868b7b35ade534c2950a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#112;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596499349\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-187\" class=\"unnumbered unstyled\" summary=\"\/\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-131e1a2ba1c868b7b35ade534c2950a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#112;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3ddbf15cd619f104d52ecc896e0a75a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"27\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596410075\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596410078\" data-type=\"exercise\">\n<div id=\"fs-id1169596410080\" data-type=\"problem\">\n<p id=\"fs-id1169596410083\">Subtract: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c9203d287587815684e1caa6cbeb36f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#109;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"98\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596410106\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596410108\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a5f9a22ab6d0d1ae71db132db00a9120_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"32\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596499254\" data-type=\"problem\">\n<p id=\"fs-id1169596499257\">Subtract: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-53800602f02829488034d4925bbf88b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;&#123;&#122;&#125;&#94;&#123;&#51;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#123;&#122;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"122\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596499286\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596499289\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0a6c129d0b1d1e95e13d6846520acf8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#123;&#122;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169596453975\">Remember that like terms must have the same variables with the same exponents.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596453982\" data-type=\"problem\">\n<p id=\"fs-id1169596453984\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f2b1f8af849d01b3d0de2bade686a0a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#123;&#99;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"108\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596454016\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-477\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f2b1f8af849d01b3d0de2bade686a0a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#123;&#99;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"108\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c2e96a51b398d55f9a68935a1e907d3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#123;&#100;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"84\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596498346\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596498349\" data-type=\"exercise\">\n<div id=\"fs-id1169596498351\" data-type=\"problem\">\n<p id=\"fs-id1169596498353\">Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-931d39f61a4e863192cb41fdc891a8d0_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;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596308850\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596308853\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-71f27d009d0036f46a8fa3f2f8593200_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<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596308882\" data-type=\"problem\">\n<p id=\"fs-id1169596308885\">Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-70db5cccbc2411a65e714b1818e3972a_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;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596499692\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596499694\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-011d52f4289763b42e782bd686d81a58_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<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596308877\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596308880\" data-type=\"exercise\">\n<div id=\"fs-id1169596499692\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596499721\" data-type=\"problem\">\n<p id=\"fs-id1169596499723\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-84e29217a044859fe097567d1361a88e_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"122\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596360371\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-77\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-84e29217a044859fe097567d1361a88e_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"122\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>There are no like terms to combine.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-84e29217a044859fe097567d1361a88e_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"122\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596499224\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596499228\" data-type=\"exercise\">\n<div id=\"fs-id1169596499230\" data-type=\"problem\">\n<p id=\"fs-id1169596499232\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c892b6a6e0c11b43045553df9a0d887a_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;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596362274\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596362277\">There are no like terms to combine.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596362288\" data-type=\"problem\">\n<p id=\"fs-id1169596362290\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-deeb024873d347b75ac90fb2a4990e4b_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;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596453918\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596453920\">There are no like terms to combine.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596308880\" data-type=\"exercise\"><\/div>\n<\/div>\n<h1>Add and Subtract Polynomials<\/h1>\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 class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596453948\" data-type=\"problem\">\n<p id=\"fs-id1169596453950\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a0b5b9bcadb86e45bee056af41a766f3_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;&#51;&#121;&#43;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#121;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"261\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596497918\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\">\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 25.4417%\">Identify like terms.<\/td>\n<td style=\"width: 74.5583%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-aab6badbccdf1d28cda5dbfb2ca31c43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#53;&#121;&#94;&#50;&#125;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#51;&#121;&#125;&#32;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#43;&#49;&#53;&#125;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"109\" style=\"vertical-align: -10px;\" \/> + <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d14913cda6884cefc84b16ff65307bac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#51;&#121;&#94;&#50;&#125;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#52;&#121;&#125;&#32;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#49;&#49;&#125;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"109\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25.4417%\">Rearrange to get the like terms together.<\/td>\n<td style=\"width: 74.5583%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b857a71360e7e46f7b16562ea7171771_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#53;&#121;&#94;&#50;&#43;&#32;&#51;&#121;&#94;&#50;&#125;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#51;&#121;&#45;&#52;&#121;&#125;&#32;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#43;&#49;&#53;&#45;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"223\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 25.4417%\">Combine like terms.<\/td>\n<td style=\"width: 74.5583%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e5b7eea9807a8b9c006a9bd6a42b02ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#121;&#94;&#50;&#45;&#55;&#121;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596378229\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596378233\" data-type=\"exercise\">\n<div id=\"fs-id1169596378235\" data-type=\"problem\">\n<p id=\"fs-id1169596378237\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-772958db74f2e3197e084b7ff602b15d_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"237\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596499124\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596499127\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-70a610eb304a7ff2e81d908aa8df8cc9_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<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596499158\" data-type=\"problem\">\n<p id=\"fs-id1169596499161\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-85ed9bcaf28afdcb8634c87575f11780_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"252\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596497040\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596497042\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-12e40709ff0f9281b7b662931d5aff1f_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<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596499152\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596499156\" data-type=\"exercise\">\n<div id=\"fs-id1169596497040\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596365153\" data-type=\"problem\">\n<p id=\"fs-id1169596365155\">Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f89126fd4ca9686403f4ea82bd1c2894_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"214\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596365206\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168745128145\" class=\"unnumbered unstyled\" summary=\"This figure has two columns. At the top of the figure, the right column contains the sum of two polynomials: 9w squared minus 7w plus 5, and 2w squared minus 4. One row down, the text in the left column says \u201cDistribute and identify like terms.\u201d The right column contains 9w squared minus 7w plus 5 minus 2w squared plus 4. 9w squared and 2w squared are identified as like terms. 5 and 4 are also identified as like terms. One row down, the text in the left column says \u201cRearrange the terms.\u201d The right column contains the earlier expression reordered so that like terms are grouped together: 9w squared minus 2w squared minus 7w plus 4 plus 4. One row down, the text in the left column says \u201cCombine like terms.\u201d The right column contains 7w squared minus 7w plus 9.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b65f4587af37a46581dec0df335bd724_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#32;&#119;&#94;&#50;&#45;&#55;&#32;&#119;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#32;&#119;&#94;&#50;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"214\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute and identify like terms.<\/td>\n<td><span id=\"eip-id1168741741686\" data-type=\"media\" data-alt=\"9 w squared and 2 w squared are like terms. 5 and 4 are also like terms.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-548c35512f18fca4dfd46bbfb2e6c9fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#57;&#32;&#119;&#94;&#50;&#125;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#55;&#32;&#119;&#125;&#43;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#115;&#105;&#109;&#125;&#123;&#53;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#50;&#32;&#119;&#94;&#50;&#125;&#125;&#43;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#115;&#105;&#109;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"189\" style=\"vertical-align: -10px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rearrange the terms.<\/td>\n<td data-align=\"left\"><span id=\"eip-id1168745057880\" data-type=\"media\" data-alt=\"9 w squared minus 2 w squared minus 7 w plus 5 plus 4.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5aded71a8f3b263fc8420848298cc04b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#57;&#32;&#119;&#94;&#50;&#45;&#50;&#32;&#119;&#94;&#50;&#125;&#125;&#32;&#45;&#32;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#55;&#32;&#119;&#125;&#43;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#115;&#105;&#109;&#125;&#123;&#53;&#125;&#43;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#115;&#105;&#109;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"189\" style=\"vertical-align: -10px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><span id=\"eip-id1168745128259\" data-type=\"media\" data-alt=\"7 w squared minus 7 w plus 9.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cc5ff6d0af279eaa1b40884e35460bc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#32;&#119;&#94;&#50;&#45;&#55;&#32;&#119;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -2px;\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596397950\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596397954\" data-type=\"exercise\">\n<div id=\"fs-id1169596397956\" data-type=\"problem\">\n<p id=\"fs-id1169596397958\">Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e70f0a59a27dffe6e57acdb8e29972fa_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"223\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596360700\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596360702\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4e75613b712bc7a53847f3b9a16cf21d_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<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596360734\" data-type=\"problem\">\n<p id=\"fs-id1169596360736\">Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f7ec25bff2efbc81ff7404ca925370ac_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"236\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596496962\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596496964\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-beca4c8856db1903b3982009fa028ef2_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<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596360727\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596360731\" data-type=\"exercise\">\n<div id=\"fs-id1169596496962\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596496988\" data-type=\"problem\">\n<p id=\"fs-id1169596496990\">Subtract: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-177d4b74d3629c2c1200fc055785e752_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#99;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"96\" style=\"vertical-align: -7px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5bdd23a9f7fc6ead8bc3ca74935fd0d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#99;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596499471\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1172187783971\" class=\"unnumbered unstyled\" style=\"height: 84px;width: 930px\" summary=\"This figure has two columns. At the top of the figure, the right column contains the difference of two trinomials: 7c squared minus 5c plus 3, minus c squared minus 4c plus 7. One row down, the text in the left column says \u201cDistribute and identify like terms.\u201d The right column contains7c squared minus 5c plus 3 minus c squared plus 4c minus 7. 7c squared and c squared are identified as like terms. Minus 5c and 4c are also identified as like terms. 3 and minus 7 are identified as like terms as well. One row down, the text in the left column says \u201cRearrange the terms.\u201d The right column contains the earlier expression reordered so that like terms are grouped together: 7c squared minus c squared minus 5c plus 4c plus 3 minus 7. One row down, the text in the left column says \u201cCombine like terms.\u201d The right column contains 6c squared minus c minus 4.\" data-label=\"\">\n<tbody>\n<tr style=\"height: 16px\">\n<td style=\"height: 16px;width: 432.597px\">Subtract: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-177d4b74d3629c2c1200fc055785e752_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#99;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"96\" style=\"vertical-align: -7px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5bdd23a9f7fc6ead8bc3ca74935fd0d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#99;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td style=\"height: 16px;width: 467.46px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1513eba803d590d551796e62b37667fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#32;&#99;&#94;&#50;&#45;&#53;&#32;&#99;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#99;&#94;&#50;&#45;&#52;&#32;&#99;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"227\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 25px\">\n<td style=\"height: 25px;width: 432.597px\">Distribute and identify like terms.<\/td>\n<td style=\"height: 25px;width: 467.46px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-19478dc5044fd91cb89c79147887a1b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#55;&#32;&#99;&#94;&#50;&#125;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#53;&#32;&#99;&#125;&#43;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#115;&#105;&#109;&#125;&#123;&#51;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#99;&#94;&#50;&#125;&#125;&#43;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#52;&#32;&#99;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#115;&#105;&#109;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"202\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 25px\">\n<td style=\"height: 25px;width: 432.597px\">Rearrange the terms.<\/td>\n<td style=\"height: 25px;width: 467.46px\" data-align=\"left\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-27eaba1b1804f078fcd11b3a1765b0e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#55;&#32;&#99;&#94;&#50;&#45;&#99;&#94;&#50;&#125;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#53;&#32;&#99;&#43;&#52;&#32;&#99;&#125;&#43;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#115;&#105;&#109;&#125;&#123;&#51;&#125;&#45;&#92;&#117;&#110;&#100;&#101;&#114;&#115;&#101;&#116;&#123;&#92;&#115;&#105;&#109;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"202\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 18px\">\n<td style=\"height: 18px;width: 432.597px\">Combine like terms.<\/td>\n<td style=\"height: 18px;width: 467.46px\"><span id=\"eip-id1172187784063\" data-type=\"media\" data-alt=\"6 c squared minus c minus 4.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-27f997136b560fa02288316efa8ed610_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#32;&#99;&#94;&#50;&#45;&#99;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"84\" style=\"vertical-align: 0px;\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596499488\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596391066\" data-type=\"exercise\">\n<div id=\"fs-id1169596391069\" data-type=\"problem\">\n<p id=\"fs-id1169596391071\">Subtract: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a37a3883ccc9ca6ba0be523c2ae3ebed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#122;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"108\" style=\"vertical-align: -7px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2025b1eedca60f8d9311acb668162be2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#122;&#45;&#52;&#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 id=\"fs-id1169596391129\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596391132\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4f7bfa75057ce8713c248c0ff0f688a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#122;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596407608\" data-type=\"problem\">\n<p id=\"fs-id1169596407610\">Subtract: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-51c3526a60dd705dc9b287316a8e2b13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"101\" style=\"vertical-align: -7px;\" \/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-216d2a28e70043038929ab90ed325dd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#120;&#45;&#49;&#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 id=\"fs-id1169596362987\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596362989\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c8763e14b4920408ebf028f1b689de8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#52;&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"107\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596407602\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596407606\" data-type=\"exercise\">\n<div id=\"fs-id1169596362987\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596363019\" data-type=\"problem\">\n<p id=\"fs-id1169596363021\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-68a831beaf30b3467f33206f23df2aa3_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"242\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596403189\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-135\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-68a831beaf30b3467f33206f23df2aa3_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"242\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-49f1dcd66bdd530f21df32b6c92506d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"213\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rearrange the terms, to put like terms together.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-40a7c72fcb09e0bab63d88ab6bd7dda1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"213\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-df62dd006150bb285ce35393682e1611_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#117;&#118;&#43;&#53;&#123;&#118;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"123\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596370437\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596370441\" data-type=\"exercise\">\n<div id=\"fs-id1169596370443\" data-type=\"problem\">\n<p id=\"fs-id1169596370446\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c919f6f543bbef47a5098d69af48d3c0_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"242\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596388052\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596388054\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0adcd39554a7e09e956fd2f4ad1728fa_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<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596388094\" data-type=\"problem\">\n<p id=\"fs-id1169596388096\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-19042bad49113014e4dde682e3d71be4_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"251\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596399239\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596399242\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dc50676680e0cdc0f4a99929b8544505_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<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596388087\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596388091\" data-type=\"exercise\">\n<div id=\"fs-id1169596399239\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596366973\" data-type=\"problem\">\n<p id=\"fs-id1169596366975\">Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-205663a8d8ea20ce7b242163036331bc_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;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"225\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596367033\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-574\" class=\"unnumbered unstyled\" summary=\"\/\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-205663a8d8ea20ce7b242163036331bc_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;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"225\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7a5a1eb94fa0564e35c31a1daf6a86ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"197\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rearrange the terms, to put like terms together.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3f85d4f2d93cd66ffbca0a9af87a7242_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"197\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-11f24bcbfff0fe7d47edca037e1dec5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596386709\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596386713\" data-type=\"exercise\">\n<div id=\"fs-id1169596386715\" data-type=\"problem\">\n<p id=\"fs-id1169596386717\">Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c621937ce36aa2defe937d3588cb1eb6_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;&#45;&#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=\"214\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596395647\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596395649\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-06f53056a8b1d24b9136eb9a838828f8_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<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596395678\" data-type=\"problem\">\n<p id=\"fs-id1169596395681\">Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8d56bb8d184d2b4226357164ad073b5e_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;&#45;&#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=\"242\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596389120\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596389122\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4eadcb6f99bac15ac566edd0e6a0bdfb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#109;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"85\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596395672\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596395676\" data-type=\"exercise\">\n<div id=\"fs-id1169596389120\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596389149\" data-type=\"problem\">\n<p id=\"fs-id1169596389152\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-08992e86a38fc604eb0f405f3be1ab30_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"284\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596362553\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-155\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-08992e86a38fc604eb0f405f3be1ab30_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"284\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5f31cc196f9c5846083eafb353278e55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"239\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rearrange the terms, to put like terms together.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-35f7fd1efaa1698fc94ebd05b59cb696_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"239\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d7a5c9ca5b4d58a52e2150d63caf7ba9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#98;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596387795\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596387799\" data-type=\"exercise\">\n<div id=\"fs-id1169596387801\" data-type=\"problem\">\n<p id=\"fs-id1169596387803\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ddefbbc1c48ca30a99ad097dff1fcb2e_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"296\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596319562\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596319564\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ba7ce0346381359e16d80170e40ebecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596319585\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596498186\" data-type=\"exercise\">\n<div id=\"fs-id1169596498188\" data-type=\"problem\">\n<p id=\"fs-id1169596498190\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b43b99d4d9aa082718afa7ab72f195af_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"286\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169596398250\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596398252\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9fba99b5df9e1a36d2c795177b160e0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#45;&#50;&#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<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596389120\" data-type=\"solution\"><\/div>\n<\/div>\n<\/div>\n<h1>Evaluate a Polynomial for a Given Value<\/h1>\n<p id=\"fs-id1169596398290\">We have already learned how to evaluate expressions. Since polynomials are expressions, we\u2019ll follow the same procedures to evaluate a <span class=\"no-emphasis\" data-type=\"term\">polynomial<\/span>. We will substitute the given value for the variable and then simplify using the order of operations.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-24c07f0475799342485254d6e2bdf9f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\" \/> when<\/p>\n<div id=\"fs-id1169596398304\" data-type=\"problem\">\n<ol id=\"fs-id1168741804270\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f7c85ff287e1ef81cbd9649e2566aada_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6b8ffae105ca6d71b769a15b83e5cd66_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;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-632442d9d0b21caa53a4c3248874daf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1169596362926\" data-type=\"solution\">\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168744362498\" class=\"unnumbered unstyled\" style=\"width: 1134px;height: 120px; width: 100%;\" summary=\"This figure has two columns. At the top of the figure, the right column contains 5x squared minus 8x plus 4. One row down, the left column says \u201cSubstitute 4 for x.\u201d The right column contains 5 times 4 squared minus 8 times 4 plus 4. One row down, the left column says \u201cSimplify the exponents.\u201d The right column contains 5 times 16 minus 8 times 4 plus 4. One row down, the left column says \u201cMultiply.\u201d The right column contains 80 minus 32 plus 4. One row down, the left column says \u201cSimplify.\u201d The right column contains 52.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 479.358px\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f7c85ff287e1ef81cbd9649e2566aada_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 622.477px\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 479.358px\"><\/td>\n<td style=\"width: 622.477px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a0a3142ac2a5e8456406e31de4693962_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#32;&#120;&#94;&#50;&#45;&#56;&#32;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 479.358px\"><span id=\"eip-id1168741859844\" data-type=\"media\" data-alt=\"Substitute negative 2 for x.\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c5c0d4e25317b5d0624d5108e764caf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> for x.<\/span><\/td>\n<td style=\"width: 622.477px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d3d13fd9bae4befe17856107a7364993_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#40;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#52;&#125;&#125;&#41;&#94;&#50;&#45;&#56;&#40;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#52;&#125;&#125;&#41;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 479.358px\">Simplify the exponents.<\/td>\n<td style=\"width: 622.477px\">\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6a2b4c61d6af257bc845fd816c01d51d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#54;&#45;&#56;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"122\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 479.358px\">Multiply.<\/td>\n<td style=\"width: 622.477px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b50b70c9a802560cde7235af8c41de70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#48;&#45;&#51;&#50;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"88\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 479.358px\">Simplify.<\/td>\n<td style=\"width: 622.477px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-043673978ce863b6cd419eb4b7a44afa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168745407360\" class=\"unnumbered unstyled\" style=\"width: 100%; width: 100%;\" summary=\"This figure has two columns. At the top of the figure, the right column contains 5x squared minus 8x plus 4. One row down, the left column says \u201cSubstitute negative 2 for x.\u201d The right column contains 5 times negative 2 squared minus 8 times negative 2 plus 4. One row down, the left column says \u201cSimplify the exponents.\u201d The right column contains 5 times 4 minus 8 times negative 2 plus 4. One row down, the left column says \u201cMultiply.\u201d The right column contains 20 plus 16 plus 4. One row down, the left column says \u201cSimplify.\u201d The right column contains 40.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 43.9929%\">b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6b8ffae105ca6d71b769a15b83e5cd66_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;\" \/><\/td>\n<td style=\"width: 55.8304%\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 43.9929%\"><\/td>\n<td style=\"width: 55.8304%\">\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a0a3142ac2a5e8456406e31de4693962_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#32;&#120;&#94;&#50;&#45;&#56;&#32;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 43.9929%\" data-align=\"left\"><span id=\"eip-id1168741859844\" data-type=\"media\" data-alt=\"Substitute negative 2 for x.\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3d1d72baf81026c5d3b1f6bba41cd7d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> for x .<\/span><\/td>\n<td style=\"width: 55.8304%\"><span id=\"eip-id1168741802146\" data-type=\"media\" data-alt=\"5 times negative 2 squared minus 8 times negative 2 plus 4.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9ddebefdd69690bf757d1cf130beb87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#40;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#50;&#125;&#125;&#41;&#94;&#50;&#45;&#56;&#40;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#45;&#50;&#125;&#125;&#41;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"151\" style=\"vertical-align: -5px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 43.9929%\">Simplify the exponents.<\/td>\n<td style=\"width: 55.8304%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5c33a225e69c2da4a7dc7355333f8b81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#45;&#56;&#32;&#40;&#45;&#50;&#41;&#32;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"128\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 43.9929%\">Multiply.<\/td>\n<td style=\"width: 55.8304%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f629a0f467a387b1379b1a78b17a58d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#43;&#49;&#54;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"88\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 43.9929%\">Simplify.<\/td>\n<td style=\"width: 55.8304%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-83acd12724cc7e741f1b085097d851eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168744046237\" class=\"unnumbered unstyled\" style=\"width: 100%; width: 100%;\" summary=\"This figure has two columns. At the top of the figure, the right column contains 5x squared minus 8x plus 4. One row down, the left column says \u201cSubstitute 0 for x.\u201d The right column contains 5 times 0 squared minus 8 times 0 plus 4. One row down, the left column says \u201cSimplify the exponents.\u201d The right column contains 5 times 0 minus 8 times 0 plus 4. One row down, the left column says \u201cMultiply.\u201d The right column contains 0 plus 0 plus 4. One row down, the left column says \u201cSimplify.\u201d The right column contains 4.\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 44.1696%\">c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-632442d9d0b21caa53a4c3248874daf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 55.742%\"><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.1696%\"><\/td>\n<td style=\"width: 55.742%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a0a3142ac2a5e8456406e31de4693962_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#32;&#120;&#94;&#50;&#45;&#56;&#32;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.1696%\" data-align=\"left\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5d3ac9faa33f207295a30283623ac18a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> for x .<\/td>\n<td style=\"width: 55.742%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b9580efe6e51d35ddab03b58e91dd0da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#40;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#48;&#125;&#125;&#41;&#94;&#50;&#45;&#56;&#40;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#48;&#125;&#125;&#41;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.1696%\">Simplify the exponents.<\/td>\n<td style=\"width: 55.742%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3bcc10694a1c7c432ab616c715d77f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#48;&#45;&#56;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#48;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"113\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.1696%\">Multiply.<\/td>\n<td style=\"width: 55.742%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-136118f4e8e124b5579235a5a8207df4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#43;&#48;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"70\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 44.1696%\">Simplify.<\/td>\n<td style=\"width: 55.742%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f1f9e2ad05c194d396ef07691cc5fdc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596396726\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596396730\" data-type=\"exercise\">\n<div id=\"fs-id1169596396732\" data-type=\"problem\">\n<p id=\"fs-id1169596396734\">Evaluate: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-05c1f7a79f731a3a98a652ed74b372ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#120;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"106\" style=\"vertical-align: -2px;\" \/> when<\/p>\n<ol id=\"fs-id1168745059161\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8f4c396d6fb5a0cd1f84a9b5871e52e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1bb30677c5fb487da7159f54afa18c34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-632442d9d0b21caa53a4c3248874daf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1169596405415\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596405417\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9763e92d302342749d971f6e3966f16d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1bab9ee4c4c271a5dbfeb6ec79cdf6e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-28baf4b08f4375fe370d40fd129e97fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"30\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596405445\" data-type=\"problem\">\n<p id=\"fs-id1169596405447\">Evaluate: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b2e8a42f2d9117610f76bd19c5bebb24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#122;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"87\" style=\"vertical-align: 0px;\" \/> when<\/p>\n<ol id=\"fs-id1168742059174\" class=\"circled\" type=\"a\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1508338f95a277fafddf12738d1dce05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3cbb4555bb9d06ea6064e06c4c2b6368_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-369f2506115009202c0b43cccfaf10ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ol>\n<\/div>\n<div id=\"fs-id1169596306478\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596306480\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9763e92d302342749d971f6e3966f16d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e46d6b69f893f0951bfb412884fb88f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-03592144ed433438101b36c930b40579_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596405439\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596405443\" data-type=\"exercise\">\n<div id=\"fs-id1169596306478\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596306506\" data-type=\"problem\">\n<p id=\"fs-id1169596306508\">The polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fa06b6513ad57cbfb3ad11917b983500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"93\" style=\"vertical-align: -2px;\" \/> gives the height of a ball <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/> 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\/math53\/wp-content\/ql-cache\/quicklatex.com-7f2b9ac40ebc1b01d5a0df3cd902df48_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 id=\"fs-id1169596361348\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-963\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fa06b6513ad57cbfb3ad11917b983500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"93\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f2b9ac40ebc1b01d5a0df3cd902df48_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;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-796b4d95cd86ec29a9e477c97d973921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"110\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1d6a41b8b531a0ed0157ea74bb474220_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#43;&#50;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"101\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-de1d402b2ef2352bfb3e1f4f64b4b202_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#52;&#43;&#50;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"79\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-24e824846ab15f7d383858c4875fb37a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>After 2 seconds the height of the ball is 186 feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596497369\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596497373\" data-type=\"exercise\">\n<div id=\"fs-id1169596497375\" data-type=\"problem\">\n<p id=\"fs-id1169596497377\">The polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fa06b6513ad57cbfb3ad11917b983500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"93\" style=\"vertical-align: -2px;\" \/> gives the height of a ball <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/> 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\/math53\/wp-content\/ql-cache\/quicklatex.com-c223c8bc198f9ee65f52e4d16dccb421_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.<\/p>\n<\/div>\n<div id=\"fs-id1169596497410\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596497413\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-cc81204035136902d16844e1041c327e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596497428\" data-type=\"problem\">\n<p id=\"fs-id1169596497431\">The polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fa06b6513ad57cbfb3ad11917b983500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"93\" style=\"vertical-align: -2px;\" \/> gives the height of a ball <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/> 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\/math53\/wp-content\/ql-cache\/quicklatex.com-665a4a37da9da24f9dab7fbbe36382c7_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 id=\"fs-id1169596369518\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596369520\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-60e5625d874dc5e57d801b2bfaa04e77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596497422\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596497426\" data-type=\"exercise\">\n<div id=\"fs-id1169596369518\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596369534\" data-type=\"problem\">\n<p id=\"fs-id1169596369536\">The polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ceb1655ccf47ecc83d3ee53c315bc80d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#53;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" 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 sides of height <em data-effect=\"italics\">y<\/em> feet. Find the cost of producing a box with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f7c85ff287e1ef81cbd9649e2566aada_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> feet and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c52f72b5459e8d0556ce651f0537f0cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/> feet.<\/p>\n<\/div>\n<div id=\"fs-id1169596314860\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168743983267\" class=\"unnumbered unstyled\" style=\"width: 890px\" summary=\"This figure has two columns. At the top of the figure, the right column contains 6x squared plus 15xy. One row down, the left column says \u201cSubstitute x equals 4, y equals 6\u201d. The right column contains 6 times 4 squared plus 15 times 4 times 6. One row down, the left column says \u201cSimplify.\u201d The right column contains 6 times 16 plus 15 times 4 times 6. One row down, the left column says \u201cSimplify.\u201d The right column contains 96 plus 360. One row down, the left column says \u201cSimplify.\u201d The right column contains 456\" data-label=\"\">\n<tbody>\n<tr>\n<td style=\"width: 523.638px\"><\/td>\n<td style=\"width: 336.425px\"><span id=\"eip-id1168743983286\" data-type=\"media\" data-alt=\"6 x squared plus 15 x y.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ceb1655ccf47ecc83d3ee53c315bc80d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#53;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" style=\"vertical-align: -4px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 523.638px\" data-align=\"left\">Substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-305efd6b2a0798a0e88ca49e5988c33a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> , <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-303985e91f898b1b1789fc75131e66fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#98;&#108;&#117;&#101;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 336.425px\"><span id=\"eip-id1168746651696\" data-type=\"media\" data-alt=\"6 times 4 squared plus 15 times 4 times 6.\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2db78ecf04215be63fd020aa7aa911f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#40;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#52;&#125;&#125;&#41;&#94;&#50;&#43;&#49;&#53;&#40;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#52;&#125;&#125;&#41;&#40;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#98;&#108;&#117;&#101;&#125;&#123;&#54;&#125;&#125;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"123\" style=\"vertical-align: -5px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 523.638px\">Simplify.<\/td>\n<td style=\"width: 336.425px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1b14adf2096dc6fca9be786e04e9fc87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#54;&#32;&#43;&#32;&#49;&#53;&#40;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#114;&#101;&#100;&#125;&#123;&#52;&#125;&#125;&#41;&#40;&#123;&#92;&#99;&#111;&#108;&#111;&#114;&#123;&#98;&#108;&#117;&#101;&#125;&#123;&#54;&#125;&#125;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 523.638px\">Simplify.<\/td>\n<td style=\"width: 336.425px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-63100739caf5308c94f228de91b22c5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#54;&#43;&#51;&#54;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"66\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 523.638px\">Simplify.<\/td>\n<td style=\"width: 336.425px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-760d073f663199e67a6368441540ea5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 523.638px\"><\/td>\n<td style=\"width: 336.425px\">The cost of producing the box is &#36;456.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596314885\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169596314889\" data-type=\"exercise\">\n<div id=\"fs-id1169596314891\" data-type=\"problem\">\n<p id=\"fs-id1169596314894\">The polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ceb1655ccf47ecc83d3ee53c315bc80d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#53;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" 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 sides of height <em data-effect=\"italics\">y<\/em> feet. Find the cost of producing a box with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-936eb2e94dcdf15a891e3a8dabc5665b_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 and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6046a2ecdf540a54a8675b9053dae1de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/> feet.<\/p>\n<\/div>\n<div id=\"fs-id1169596365368\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596365370\">&#36;576<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169596365383\" data-type=\"problem\">\n<p id=\"fs-id1169596365385\">The polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ceb1655ccf47ecc83d3ee53c315bc80d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#53;&#120;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"85\" 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 sides of height <em data-effect=\"italics\">y<\/em> feet. Find the cost of producing a box with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-50e8b7c71a6ee61f7cae4d74eccc7bac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/> feet and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a5af5385cf9d587645b75f10cf74a28f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/> feet.<\/p>\n<\/div>\n<div id=\"fs-id1169596365439\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169596365441\">&#36;750<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596374921\" class=\"media-2\" data-type=\"note\">\n<p id=\"fs-id1169596374925\">Access these online resources for additional instruction and practice with adding and subtracting polynomials.<\/p>\n<ul id=\"fs-id1169596374929\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/25Addsubtrpoly1\">Add and Subtract Polynomials 1<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25Addsubtrpoly2\">Add and Subtract Polynomials 2<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25Addsubtrpoly3\">Add and Subtract Polynomial 3<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25Addsubtrpoly4\">Add and Subtract Polynomial 4<\/a><\/li>\n<\/ul>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1169596374969\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Monomials<\/strong>\n<ul id=\"fs-id1169596374981\" data-bullet-style=\"open-circle\">\n<li>A monomial is a term of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b1f34ffb1b277daca10222d739f07a74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#123;&#120;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_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;\" \/> is a constant and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e2ab2eed1ecd297014b27aaa529e23c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> is a whole number<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Polynomials<\/strong>\n<ul id=\"fs-id1169596497714\" data-bullet-style=\"open-circle\">\n<li><strong data-effect=\"bold\">polynomial<\/strong>\u2014A monomial, or two or more monomials 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>\u2014A 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-id1171791456751\" data-bullet-style=\"open-circle\">\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<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1169596390906\">\n<dt>binomial<\/dt>\n<dd id=\"fs-id1169596390912\">A binomial is a polynomial with exactly two terms.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169596390916\">\n<dt>degree of a constant<\/dt>\n<dd id=\"fs-id1169596390921\">The degree of any constant is 0.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169596390925\">\n<dt>degree of a polynomial<\/dt>\n<dd id=\"fs-id1169596390931\">The degree of a polynomial is the highest degree of all its terms.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169596390935\">\n<dt>degree of a term<\/dt>\n<dd id=\"fs-id1169596390940\">The degree of a term is the exponent of its variable.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169596390945\">\n<dt>monomial<\/dt>\n<dd id=\"fs-id1169596390950\">A monomial is a term of the form <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b1f34ffb1b277daca10222d739f07a74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#123;&#120;&#125;&#94;&#123;&#109;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e9c4cc6ee8914c6fb4d5253abf7fc46_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;\" \/> is a constant and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e2ab2eed1ecd297014b27aaa529e23c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\" \/> is a whole number; a monomial has exactly one term.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169596380528\">\n<dt>polynomial<\/dt>\n<dd id=\"fs-id1169596380533\">A polynomial is a monomial, or two or more monomials combined by addition or subtraction.<\/dd>\n<\/dl>\n<dl id=\"fs-id1169596380539\">\n<dt>standard form<\/dt>\n<dd id=\"fs-id1169596380544\">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-id1169596380549\">\n<dt>trinomial<\/dt>\n<dd id=\"fs-id1169596380555\">A trinomial is a polynomial with exactly three terms.<\/dd>\n<\/dl>\n<p>Type your textbox content here.<\/p>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1169596367644\" style=\"text-align: left\">Identify Polynomials, Monomials, Binomials, and Trinomials<\/h2>\n<p id=\"fs-id1168741892941\">In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">\n<p id=\"fs-id1166426192935\">1.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9ea640a12969b00e37d55479de58462c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#45;&#50;&#52;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"117\" style=\"vertical-align: -2px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e03dfb3444a8795a8a4fe5dc0e52bff6_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;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f579d236cb682a8fad39f86e1642abc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#125;&#123;&#49;&#53;&#125;&#121;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"62\" style=\"vertical-align: -12px;\" \/><br \/>\nd) 5<br \/>\ne) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ac2fc617e3232f6ebdabf2be3ba2bea4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#121;&#43;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"58\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%\">\n<p id=\"fs-id1166425964014\">2.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e6f921917ef2d967a3c6ad62e798bbec_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;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2535c8387892bb4a1314d7c1358fcde9_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=\"15\" width=\"46\" style=\"vertical-align: 0px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-255ef6c3e2f5c8952afbf050114a071d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -2px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3ea18efba757ba68beda07a6bc5ae294_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#120;&#121;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -4px;\" \/><br \/>\ne) 19<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">\n<p id=\"fs-id1166426185366\">3.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c06243c570f90652098094c18759066c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-06384a972d2bb8c3bed9642311c2456d_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;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-370003f484cdf67e66acf6314dfacb4a_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;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9ea640a12969b00e37d55479de58462c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#49;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#45;&#50;&#52;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"117\" style=\"vertical-align: -2px;\" \/><br \/>\ne) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-619f6c87a1d747b4d84a94773f9f66c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%\">\n<p id=\"fs-id1166426272537\">4.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9c842f2b5b8c76ed802ea0013b03eeac_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;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a752afc1f88d2084819dd58f9a502144_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;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2b8a28f0e7ca3e7ff135aad24bdbfc8d_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;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ac2fc617e3232f6ebdabf2be3ba2bea4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#121;&#43;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"58\" style=\"vertical-align: -4px;\" \/><br \/>\ne) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e03dfb3444a8795a8a4fe5dc0e52bff6_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;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596499577\" style=\"text-align: left\"><strong data-effect=\"bold\"><br \/>\n<\/strong>Determine the Degree of Polynomials<\/h2>\n<p id=\"fs-id1168741855043\">In the following exercises, determine the degree of each polynomial.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 266px\">\n<tbody>\n<tr style=\"height: 140px\">\n<td style=\"width: 50%;height: 140px\">\n<p id=\"fs-id1166425926085\">5.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7e1e40652bdca0b9c9e1b3fc808a9368_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#97;&#43;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"114\" style=\"vertical-align: -2px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4fb3c6c3bcfcf2ac6f4562e39bf32bd4_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;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d62acacbdef10a24b82724317c3f448f_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;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-370003f484cdf67e66acf6314dfacb4a_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;\" \/><br \/>\ne) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0441ed6bcb323d34e2f5589422a41e45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 140px\">\n<p id=\"fs-id1166426253457\">6.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-57ed5239ea4739e41c93b0a3cd210d43_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;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c41fbee46e716511e7615538917c45bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#50;&#123;&#112;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -4px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ede5034ddb769044ee2d7281c9e95f5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#97;&#43;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"97\" style=\"vertical-align: -2px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a9c93d749ca1f71986f149e57f6b49d6_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;\" \/><br \/>\ne) 17<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">\n<p id=\"fs-id1166425935275\">7.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4727b45e49874d16948aa6ad35a33aff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#45;&#50;&#57;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"66\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-06384a972d2bb8c3bed9642311c2456d_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;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-370003f484cdf67e66acf6314dfacb4a_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;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ebb1132e57d7b3743e5d58e7dd256781_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=\"15\" width=\"82\" style=\"vertical-align: 0px;\" \/><br \/>\ne) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5cac4bc2f960e6a9754ddf4913c65741_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;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">\n<p id=\"fs-id1166425972094\">8.<\/p>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ed738a801b947a7beccea81f9179e3dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#50;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"34\" style=\"vertical-align: -4px;\" \/><br \/>\nb) 15<br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2b8a28f0e7ca3e7ff135aad24bdbfc8d_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;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c9ad6ed9347a2ad0784c7ddfc7395e97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#45;&#57;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"57\" style=\"vertical-align: 0px;\" \/><br \/>\ne) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8f377876d8130e9d406b9f625b270c45_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;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596372469\" style=\"text-align: left\"><strong data-effect=\"bold\"><br \/>\n<\/strong>Add and Subtract Monomials<\/h2>\n<p id=\"fs-id1168745505449\">In the following exercises, add or subtract the monomials.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 140px\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-31e88871828aea2c9734b698718b84ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#55;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"74\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e2cb550bb048f8dde5e2caaf642820ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#52;&#121;&#125;&#94;&#123;&#51;&#125;&#43;&#54;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b7110fc0535b7e4cc7aa82bb298d8190_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;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e36d0c2970ce2525825e41275073b5e3_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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7ba17603e66d71c608c82e7ea364e485_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e7f2dbf211e204e574770036afe31af6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#121;&#45;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"62\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3b4419d6fb842fd234020f78b51b3dd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#56;&#120;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-93e7a576abf8b2a8a0bd9fee5ce4ddbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;&#122;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#122;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4c09a8d517eee11c7e5c93ea10019624_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#98;&#45;&#49;&#55;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"77\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-80dbaa37a46a93551a01f79efdf7b9c6_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=\"13\" width=\"90\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-af71ce04bceacb953f172b3d05f2db29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#97;&#43;&#53;&#98;&#45;&#50;&#50;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"113\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-628c84916e9302daa1eb7a101588af01_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-26362e44dc34fe6231f5f4c13c99c66d_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;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e0e1c9d5dd9323d229d09f1f4b99447a_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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-13a7a0b83c908dc353647cd9f2fe954c_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;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-535ef7c73c2764465e98cd4c159df9f9_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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8db6d6e57d7c675248d241325091bb71_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=\"15\" width=\"119\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f12f3ee7a03a02e048f557c513cca260_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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e0f7f5235ec7333d0e8fca00c08eb1c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#97;&#125;&#43;&#56;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"64\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f6189cbab1d6e129646fa80757d568a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#57;&#121;&#125;&#43;&#53;&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">29. Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c4f5d9b668d9133732c5a007cc84e5cc_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=\"16\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%\">30. Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bf1ae0dd57abb35caae5312618fa9725_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#44;&#51;&#121;&#44;&#45;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"86\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">31. Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-549a29e8ea6dc49aacac0990a01f9e1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#54;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#114;&#111;&#109;&#125;&#45;&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"119\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 50%\">32. Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6db540d3de5e5e34a275d9c4a2ee7727_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#114;&#111;&#109;&#125;&#45;&#55;&#123;&#112;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"108\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596402107\" style=\"text-align: left\">Add and Subtract Polynomials<\/h2>\n<p id=\"fs-id1168742190618\">In the following exercises, add or subtract the polynomials.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-23b64a303ad081f6e17fb1147f0bfe61_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;\" \/><\/td>\n<td style=\"width: 50%\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b822f9f4230792a6c7d1bec5df2faade_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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2fbe7ff271d2a10de4f1a33da644dd95_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;\" \/><\/td>\n<td style=\"width: 50%\">36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bc11a340877d4cf0554677bd78429bde_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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-313175301241ad38e67ca1ccf0c3b6a6_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;\" \/><\/td>\n<td style=\"width: 50%\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f8f82fc0d0e9da2feaf2c60efde897fe_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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9fcf234a61ebd12f621484e2c9aedec9_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;\" \/><\/td>\n<td style=\"width: 50%\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c231879bb4e8e8310223fb4ade4759d5_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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f5fe45301dfc47332cb5c873fb3330b7_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;\" \/><\/td>\n<td style=\"width: 50%\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-514302be0ae05d9ec25659e74a313571_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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-519e9c4dbdc838f629e0139f599800ee_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;\" \/><\/td>\n<td style=\"width: 50%\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4cd8d40f2e6ec70595e6c50e635aee51_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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8a67d8ab6196d601469d9c9aa30b9ae9_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;\" \/><\/td>\n<td style=\"width: 50%\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0cc0b5b6734061a85b21623ca30c8430_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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">47. Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ff6613591c4ca4c812e865df8fc7cd49_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\/math53\/wp-content\/ql-cache\/quicklatex.com-31499ecc3df0bde6e3a12279eeb62057_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;\" \/>.<\/td>\n<td style=\"width: 50%\">48. Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0980e240f6a1b095aa43f914930fb177_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\/math53\/wp-content\/ql-cache\/quicklatex.com-c3835e589cc23d6146e1e5bdc0ec2135_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;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">49. Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ce2ccfe16d7aabaa34778a2ca5c78e0a_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\/math53\/wp-content\/ql-cache\/quicklatex.com-b94078bdd39ed181cec62926f43402ce_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;\" \/>.<\/td>\n<td style=\"width: 50%\">50. Subtract <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-11c4ab28ba9d87ba6060300555b7fb88_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\/math53\/wp-content\/ql-cache\/quicklatex.com-18e2e3fa4b68b4d0b5d1c3131ed760ec_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;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">51. Find the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5ceb92afc34f441bf82e73be0a2472ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -7px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-060a0d5eed83356ee2519bb95e7c4a38_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;&#57;&#112;&#43;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"108\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td style=\"width: 50%\">52. Find the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a8c7dcd1f9cb0a646c4d69843b1ee024_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#113;&#43;&#49;&#51;&#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\/math53\/wp-content\/ql-cache\/quicklatex.com-c4237b2cd1923679fc9a45b83e73ed49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">53. Find the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c6124a218ffe21478018e24570e45560_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#45;&#56;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"78\" style=\"vertical-align: -7px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-aad5c995c3198f9a6934715c410cbb0c_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;&#54;&#97;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"109\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td style=\"width: 50%\">54. Find the sum of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-20113c1404a4d3aaef30849caa6d89ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#98;&#43;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -7px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-57f06932bd120d8581d55b6fdf22447e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"67\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">55. Find the difference of<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a55febb6a2e59b510f120a09b784f5bc_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<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5c3cb5cb880600b983d52ea56a1dc411_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;\" \/>.<\/td>\n<td style=\"width: 50%\">56. Find the difference of<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4a2a205ffed9b2ba0e852d82ea01f9b6_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<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-58456450a570504f78fb609a62f22cb6_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;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">57. Find the difference of<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-74ba00a709f610a3da2ef1d511af6696_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#99;&#45;&#51;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -7px;\" \/> and<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-315cd2084b698f9bcbade6ca50ea5b16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#99;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"105\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<td style=\"width: 50%\">58. Find the difference of<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8f68f1e850214c277552337ab82e0bce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#116;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"103\" style=\"vertical-align: -7px;\" \/> and<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5ac21d2de6c62ed5b7a46c4c8881463f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#116;&#45;&#49;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"103\" style=\"vertical-align: -7px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-33c461d493d312b90f55cf18df61a687_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;\" \/><\/td>\n<td style=\"width: 50%\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9a0e1c402bf5030af31f1f40e9f733b6_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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1bb83aec817570cca20293fa60de4f8b_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;\" \/><\/td>\n<td style=\"width: 50%\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2aed88d265876ca84fc3205328d8a08e_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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-93605195d1bbd594dd93b136f227adec_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;\" \/><\/td>\n<td style=\"width: 50%\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8c7de2e94dae6f648b3457c26c14e163_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;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-92784d8e7a5bd3aa112c615df84ecc79_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;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#117;&#118;&#45;&#51;&#123;&#118;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"222\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6732c5a5eda31d432b69780793e74b11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#106;&#125;&#94;&#123;&#50;&#125;&#45;&#123;&#107;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#106;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#106;&#107;&#45;&#53;&#123;&#107;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"218\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2a6a5ff451c647980270c8348dbf4b09_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"203\" style=\"vertical-align: -7px;\" \/><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-85f06238bd52eace7c2b914d6989f855_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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=\"111\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">68. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d5f3d6d8745a01053aec1b8d62d7d0ca_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"184\" style=\"vertical-align: -7px;\" \/><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2a8c3ca45b0c3a52601d0b2a78e603fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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=\"119\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-81f3681aae75a95b19de4e4ff3b33e5b_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"191\" style=\"vertical-align: -7px;\" \/><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8b4e91c37111e600b2c914b21302a42d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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=\"116\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">70. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-46ce918e6b59b3acee2529df16bf24b2_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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"200\" style=\"vertical-align: -7px;\" \/><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f3cb1101b5f320e640aa55f4cb370087_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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=\"115\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1169596411950\" style=\"text-align: left\">Evaluate a Polynomial for a Given Value<\/h2>\n<p id=\"fs-id1168742058387\">In the following exercises, evaluate each polynomial for the given value.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 235px\">\n<tbody>\n<tr style=\"height: 123px\">\n<td style=\"width: 50%;height: 123px\">\n<div id=\"fs-id1169596411958\" data-type=\"exercise\">\n<div id=\"fs-id1169596411960\" data-type=\"problem\">\n<p id=\"fs-id1169596411962\">71. Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-60a4e3a952b23f1147e7d7e75cebcaf1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#121;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"95\" style=\"vertical-align: -4px;\" \/> when:<\/p>\n<p id=\"fs-id1166423871629\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c5b52ab06c98188240767bfa31f6bda8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"41\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-095aaa35b3f195382db21bd047c2fae5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f04047b91e09f49c77388d57afc19622_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596455663\" data-type=\"exercise\">\n<div id=\"fs-id1169596455665\" data-type=\"problem\">\n<p id=\"fs-id1169596455667\">\n<\/div>\n<\/div>\n<\/td>\n<td style=\"width: 50%;height: 123px\">\n<div id=\"fs-id1169596455663\" data-type=\"exercise\">\n<div id=\"fs-id1169596455665\" data-type=\"problem\">\n<p id=\"fs-id1169596455667\">72. Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f8215041a2c3717c83804702f8d9e873_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#121;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -4px;\" \/> when:<\/p>\n<p id=\"fs-id1166425960377\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-181500ee3442dd1157f28285e7af15a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"56\" style=\"vertical-align: -4px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-19434dd9950830cd60f98505c47d0591_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f04047b91e09f49c77388d57afc19622_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1169596455733\" data-type=\"exercise\">\n<div id=\"fs-id1169596455736\" data-type=\"problem\">\n<p id=\"fs-id1169596455738\">\n<\/div>\n<\/div>\n<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">\n<p id=\"fs-id1169596455738\">73. Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b69d1f90d6b4da6e5b33ea1fe2811b03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#45;&#51;&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"59\" style=\"vertical-align: 0px;\" \/> when:<\/p>\n<p id=\"fs-id1166423760338\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8f4c396d6fb5a0cd1f84a9b5871e52e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-632442d9d0b21caa53a4c3248874daf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9b8f88fb8f9477ee4a3065de5d8c2ff6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/td>\n<td style=\"width: 50%;height: 14px\">\n<p id=\"fs-id1169596455802\">74. Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-617e23324531a7a007a51e748e09aa38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#45;&#51;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: 0px;\" \/> when:<\/p>\n<p id=\"fs-id1166426184684\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9b8f88fb8f9477ee4a3065de5d8c2ff6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"56\" style=\"vertical-align: 0px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-632442d9d0b21caa53a4c3248874daf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/><br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4364c0939f009d3cf1c30d8c09c80805_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">75. A painter drops a brush from a platform 75 feet high. The polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-91c6ab1069fa5efef34b5b0c0762ce39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"83\" style=\"vertical-align: -2px;\" \/> gives the height of the brush <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/> seconds after it was dropped. Find the height after <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f2b9ac40ebc1b01d5a0df3cd902df48_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.<\/td>\n<td style=\"width: 50%;height: 14px\">76. A girl drops a ball off a cliff into the ocean. The polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fa06b6513ad57cbfb3ad11917b983500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"93\" style=\"vertical-align: -2px;\" \/> gives the height of a ball <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/> seconds after it is dropped from a 250-foot tall cliff. Find the height after <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7f2b9ac40ebc1b01d5a0df3cd902df48_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.<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">77. 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 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-820700bcbadd60655fdb94f8f9133660_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#50;&#48;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -4px;\" \/>. Find the revenue received when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8822460a579da1380a91d72763ae4189_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.<\/td>\n<td style=\"width: 50%;height: 14px\">78. 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\/math53\/wp-content\/ql-cache\/quicklatex.com-820700bcbadd60655fdb94f8f9133660_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#50;&#48;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -4px;\" \/>. Find the revenue received when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d4754d0c2d9a9727f7e2fc0670bcc06e_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.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">79. <strong data-effect=\"bold\">Fuel Efficiency<\/strong> The fuel efficiency (in miles per gallon) of a car going at a speed of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bb53ce30a3ff5b6ca87fc6e1eb6588a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> miles per hour is given by the polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d2981ea288abfc1f95b8b41b9aab2090_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#53;&#48;&#125;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"106\" style=\"vertical-align: -12px;\" \/>. Find the fuel efficiency when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-673506b577f7dd8746c5ff70a8f20ad7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#51;&#48;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#112;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<td style=\"width: 50%\">80.<strong data-effect=\"bold\"> Stopping Distance<\/strong> The number of feet it takes for a car traveling at <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bb53ce30a3ff5b6ca87fc6e1eb6588a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> miles per hour to stop on dry, level concrete is given by the polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-246a666ee95867a19a3d946e23a65502_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#48;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#46;&#49;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"104\" style=\"vertical-align: -2px;\" \/>. Find the stopping distance when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f707e4ca165be5023ff7349a2b051533_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#52;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#112;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"87\" style=\"vertical-align: -4px;\" \/>.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">81.<strong data-effect=\"bold\"> Rental Cost<\/strong> The cost to rent a rug cleaner for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b8bfee3a85664394921a77e26dc3b4bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\" \/> days is given by the polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9cf49efec115b9991b428a75ebc96382_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#46;&#53;&#48;&#100;&#43;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"79\" style=\"vertical-align: -2px;\" \/>. Find the cost to rent the cleaner for 6 days.<\/td>\n<td style=\"width: 50%\">82.<strong data-effect=\"bold\"> Height of Projectile<\/strong> The height (in feet) of an object projected upward is given by the polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6ab21842c43c5b90899cf3910d51107f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#54;&#123;&#116;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#48;&#116;&#43;&#57;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"130\" style=\"vertical-align: -2px;\" \/> where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9af0c8da890e2a109be7d30ff271872_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\" \/> represents time in seconds. Find the height after <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c719ce4edf4e1d2e20cd0ea6b1579b6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;&#61;&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"52\" style=\"vertical-align: 0px;\" \/> seconds.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">83.<strong data-effect=\"bold\"> Temperature Conversion<\/strong> The temperature in degrees Fahrenheit is given by the polynomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ed0264a7706eb82354d17f3a8043088e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#53;&#125;&#99;&#43;&#51;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"57\" style=\"vertical-align: -12px;\" \/> where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-77479b59a494b611004da289deb0dfa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> represents the temperature in degrees Celsius. Find the temperature in degrees Fahrenheit when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9736c2004e648830e8a58739e45e8e06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#61;&#54;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: 0px;\" \/>\u00b0.<\/td>\n<td style=\"width: 50%\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 data-type=\"title\">Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">84. Using your own words, explain the difference between a monomial, a binomial, and a trinomial.<\/td>\n<td style=\"width: 50%\">85. Using your own words, explain the difference between a polynomial with five terms and a polynomial with a degree of 5.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">86. Ariana thinks the sum <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-64138a5e8c005321b22ee126e55a944b_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\/math53\/wp-content\/ql-cache\/quicklatex.com-ab016ea299eaedb86d6b93c5ad08636a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#123;&#121;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"33\" style=\"vertical-align: -4px;\" \/>. What is wrong with her reasoning?<\/td>\n<td style=\"width: 50%\">87. Jonathan thinks that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e791559947bd095c38384830ce5e4ff5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"9\" style=\"vertical-align: -12px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-92499353ef001517fc5e19b0d3eb4030_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"11\" style=\"vertical-align: -12px;\" \/> are both monomials. What is wrong with his reasoning?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse;width: 100%;height: 371px\">\n<tbody>\n<tr style=\"height: 34px\">\n<td style=\"width: 50%;height: 34px\">1. a) trinomial b) polynomial c) binomial d) monomial e) binomial<\/td>\n<td style=\"width: 50%;height: 34px\">3. a) binomial b) trinomial c) polynomial d) trinomial e) monomial<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">5. a) 2 b) 4 c) 1 d) 3 e) 0<\/td>\n<td style=\"width: 50%;height: 16px\">7. a) 1 b) 2 c) 3 d) 3 e) 0<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-63c01d81dd66441564ed869518a05496_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5726d2ae140651962d0e116af42a2726_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-54104dfe01eac6c7f9a064f7ef57dbc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9cbb0b99651fda0ef28d0a7c24fbf9a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9691d0d50ad1bd6661a43e51169ae73a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#50;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"39\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a4b621fc456c9bd596bb9b93b528db75_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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6ea8b372e552109355900fab50e935dd_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;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-13a7a0b83c908dc353647cd9f2fe954c_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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8db6d6e57d7c675248d241325091bb71_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=\"15\" width=\"119\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e0f7f5235ec7333d0e8fca00c08eb1c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#97;&#125;&#43;&#56;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"64\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2139a77be9404fbec520a846850644d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#97;&#45;&#51;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"70\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-be93271ada4820ecd65f0dad461a089c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#55;&#123;&#120;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-be31847044a1b216d842ee1003aaebc9_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;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-37a2dc1721ca3b3c332825593cb1b58f_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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-48b8233cae433e9f875c5a1afe4b5280_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;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2a3e9ede2c1c46e52ef2cd1e8f0ebda6_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=\"15\" width=\"95\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e16d698b86d427e187702dc6d5783f99_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;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9217386de0b427ecaa4ec74c82492c1a_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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px\">\n<td style=\"width: 50%;height: 17px\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fb181823a70c04a251157769e9e3b113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#54;&#115;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"111\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 17px\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-544a42b177348b59876b924652b564f4_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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-90fe80ccde160deb61cec7702343f843_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;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3b849695cdfa5f9b6d0f6fb2aa6f9d01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#43;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#112;&#43;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-765dca915da696d4ff9f1b6104cf5200_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#43;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#97;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"143\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-146554ff1028e1676bdd0c435ff96893_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#119;&#45;&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"70\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1d138cb51c589ba0839cd146e98b313c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#99;&#45;&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"63\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-938d5ebcadf2508b8e67df53e4846868_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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-24a9213bb5da43bf144873f641097ad7_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;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-42e312cc375eba5263d479334c2f8592_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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1188497a74f891293af8244eaceb2dc2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#117;&#118;&#43;&#50;&#123;&#118;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"75\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-86c73369158906ed7aacc243d27a1263_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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9acf5a871fc7177bbccb0d688392eceb_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;\" \/><\/td>\n<td style=\"width: 50%;height: 16px\">71. a) 187 b) 40 c) 2<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">73. a) \u2212104 b) 4 c) 40<\/td>\n<td style=\"width: 50%;height: 16px\">75. 11<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">77. &#36;10,800<\/td>\n<td style=\"width: 50%;height: 16px\">79. 4 miles per gallon<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">81. &#36;58<\/td>\n<td style=\"width: 50%;height: 16px\">83. 149<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 50%;height: 16px\">85. Answers will vary.<\/td>\n<td style=\"width: 50%;height: 16px\">87. Answers will vary.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cAdd and Subtract Polynomials\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n<p><!-- pb_fixme --><\/p>\n","protected":false},"author":999,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-1685","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":1647,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1685","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":15,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1685\/revisions"}],"predecessor-version":[{"id":2653,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1685\/revisions\/2653"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/parts\/1647"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1685\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/media?parent=1685"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapter-type?post=1685"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/contributor?post=1685"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/license?post=1685"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}