{"id":2992,"date":"2018-12-11T13:50:45","date_gmt":"2018-12-11T18:50:45","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/chapter\/greatest-common-factor-and-factor-by-grouping\/"},"modified":"2018-12-11T13:50:45","modified_gmt":"2018-12-11T18:50:45","slug":"greatest-common-factor-and-factor-by-grouping","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/chapter\/greatest-common-factor-and-factor-by-grouping\/","title":{"raw":"Greatest Common Factor and Factor by Grouping","rendered":"Greatest Common Factor and Factor by Grouping"},"content":{"raw":"\n[latexpage]<div class=\"textbox textbox--learning-objectives\"><h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>By the end of this section, you will be able to: <ul><li>Find the greatest common factor of two or more expressions<\/li><li>Factor the greatest common factor from a polynomial<\/li><li>Factor by grouping<\/li><\/ul><\/div><div data-type=\"note\" id=\"fs-id1167835305786\" class=\"be-prepared\"><p id=\"fs-id1167835420924\">Before you get started, take this readiness quiz.<\/p><ol id=\"fs-id1167835236318\" type=\"1\"><li>Factor 56 into primes.<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167829937177\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>Find the least common multiple (LCM) of 18 and 24.<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167829937221\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><li>Multiply: \\(-3a\\left(7a+8b\\right).\\)<div data-type=\"newline\"><br><\/div> If you missed this problem, review <a href=\"\/contents\/0b9be1db-21c4-4bd0-8f8e-d809f6ff7c8c#fs-id1167829810683\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li><\/ol><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167832153812\"><h3 data-type=\"title\">Find the Greatest Common Factor of Two or More Expressions<\/h3><p id=\"fs-id1167835380264\">Earlier we multiplied factors together to get a <span data-type=\"term\" class=\"no-emphasis\">product<\/span>. Now, we will reverse this process; we will start with a product and then break it down into its factors. Splitting a product into factors is called <span data-type=\"term\">factoring<\/span>.<\/p><span data-type=\"media\" id=\"fs-id1167834228697\" data-alt=\"8 times 7 is 56. Here 8 and 7 are factors and 56 is the product. An arrow pointing from 8 times 7 to 56 is labeled multiply. An arrow pointing from 56 to 8 times 7 is labeled factor. 2x open parentheses x plus 3 close parentheses equals 2x squared plus 6x. Here the left side of the equation is labeled factors and the right side is labeled products.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_001_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"8 times 7 is 56. Here 8 and 7 are factors and 56 is the product. An arrow pointing from 8 times 7 to 56 is labeled multiply. An arrow pointing from 56 to 8 times 7 is labeled factor. 2x open parentheses x plus 3 close parentheses equals 2x squared plus 6x. Here the left side of the equation is labeled factors and the right side is labeled products.\"><\/span><p id=\"fs-id1167835339323\">We have learned how to factor numbers to find the least common multiple (LCM) of two or more numbers. Now we will factor expressions and find the <span data-type=\"term\">greatest common factor<\/span> of two or more expressions. The method we use is similar to what we used to find the LCM.<\/p><div data-type=\"note\" id=\"fs-id1167834092857\"><div data-type=\"title\">Greatest Common Factor<\/div><p id=\"fs-id1167834195947\">The <strong data-effect=\"bold\">greatest common factor<\/strong> (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.<\/p><\/div><p id=\"fs-id1167834284447\">We summarize the steps we use to find the greatest common factor.<\/p><div data-type=\"note\" id=\"fs-id1167832065589\" class=\"howto\"><div data-type=\"title\">Find the greatest common factor (GCF) of two expressions.<\/div><ol id=\"fs-id1167835377721\" type=\"1\" class=\"stepwise\"><li>Factor each coefficient into primes. Write all variables with exponents in expanded form.<\/li><li>List all factors\u2014matching common factors in a column. In each column, circle the common factors.<\/li><li>Bring down the common factors that all expressions share.<\/li><li>Multiply the factors.<\/li><\/ol><\/div><p id=\"fs-id1167826782766\">The next example will show us the steps to find the greatest common factor of three expressions.<\/p><div data-type=\"example\" id=\"fs-id1167835345627\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167826864261\"><div data-type=\"problem\" id=\"fs-id1167835304441\"><p id=\"fs-id1167835328287\">Find the greatest common factor of \\(21{x}^{3},9{x}^{2},15x.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834111768\"><table id=\"fs-id1167832056779\" class=\"unnumbered unstyled\" summary=\"The terms are 21 x cubed, 9 x squared and 15 x. The first step is to factor each coefficient into primes and write the variables with exponents in expanded form. 21 x cubed is written as 3 times 7 times x times x times x. 9 x squared is written as 3 times 3 times x times x. 15 x is written as 3 times 5 times x. Now bring down the common factors. So, GCF is 3 times x. Now multiply the factors. So, GCF of 21 x cubed, 9 x squared and 15x is 3x.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Factor each coefficient into primes and write the<div data-type=\"newline\"><br><\/div>variables with exponents in expanded form.<div data-type=\"newline\"><br><\/div>Circle the common factors in each column.<div data-type=\"newline\"><br><\/div>Bring down the common factors.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835198732\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_002a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Multiply the factors.<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167826927120\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_002b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\">The GCF of \\(21{x}^{3}\\), \\(9{x}^{2}\\) and \\(15x\\) is \\(3x\\).<\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167834432356\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167830838256\"><div data-type=\"problem\" id=\"fs-id1167834196401\"><p id=\"fs-id1167831910334\">Find the greatest common factor: \\(25{m}^{4},35{m}^{3},20{m}^{2}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834538418\"><p id=\"fs-id1167835214252\">\\(5{m}^{2}\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167834510590\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167831112380\"><div data-type=\"problem\" id=\"fs-id1167835331913\"><p>Find the greatest common factor: \\(14{x}^{3},70{x}^{2},105x.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835341858\"><p id=\"fs-id1167835368345\">\\(7x\\)<\/p><\/div><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167834124439\"><h3 data-type=\"title\">Factor the Greatest Common Factor from a Polynomial<\/h3><p id=\"fs-id1167835421146\">It is sometimes useful to represent a number as a product of factors, for example, 12 as \\(2\u00b76\\) or \\(3\u00b74.\\) In algebra, it can also be useful to represent a polynomial in factored form. We will start with a product, such as \\(3{x}^{2}+15x,\\) and end with its factors, \\(3x\\left(x+5\\right).\\) To do this we apply the Distributive Property \u201cin reverse.\u201d<\/p><p id=\"fs-id1167835304585\">We state the Distributive Property here just as you saw it in earlier chapters and \u201cin reverse.\u201d<\/p><div data-type=\"note\" id=\"fs-id1167835216215\"><div data-type=\"title\">Distributive Property<\/div><p id=\"fs-id1167832195752\">If <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em> are real numbers, then<\/p><div data-type=\"equation\" id=\"fs-id1167832054886\" class=\"unnumbered\" data-label=\"\">\\(a\\left(b+c\\right)=ab+ac\\phantom{\\rule{1em}{0ex}}\\text{and}\\phantom{\\rule{1em}{0ex}}ab+ac=a\\left(b+c\\right)\\)<\/div><p id=\"fs-id1167834279599\">The form on the left is used to multiply. The form on the right is used to factor.<\/p><\/div><p>So how do you use the Distributive Property to factor a <span data-type=\"term\" class=\"no-emphasis\">polynomial<\/span>? You just find the GCF of all the terms and write the polynomial as a product!<\/p><div data-type=\"example\" id=\"fs-id1167835380170\" class=\"textbox textbox--examples\"><div data-type=\"title\">How to Use the Distributive Property to factor a polynomial<\/div><div data-type=\"exercise\" id=\"fs-id1167826994118\"><div data-type=\"problem\" id=\"fs-id1167835214077\"><p id=\"fs-id1167834516153\">Factor: \\(8{m}^{3}-12{m}^{2}n+20m{n}^{2}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834494820\"><span data-type=\"media\" id=\"fs-id1167831920033\" data-alt=\"Step 1 is find the GCF of all the terms in the polynomial. GCF of 8 m cubed, 12 m squared n and 20 mn squared is 4m.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_003a_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is find the GCF of all the terms in the polynomial. GCF of 8 m cubed, 12 m squared n and 20 mn squared is 4m.\"><\/span><span data-type=\"media\" id=\"fs-id1167835280158\" data-alt=\"Step 1 is find the GCF of all the terms in the polynomial. GCF of 8 m cubed, 12 m squared n and 20 mn squared is 4m.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_003b_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is find the GCF of all the terms in the polynomial. GCF of 8 m cubed, 12 m squared n and 20 mn squared is 4m.\"><\/span><span data-type=\"media\" id=\"fs-id1167832046576\" data-alt=\"In step 3, use the reverse Distributive Property to factor the expression as 4m open parentheses 2 m squared minus 3 mn plus 5 n squared close parentheses.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_003c_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"In step 3, use the reverse Distributive Property to factor the expression as 4m open parentheses 2 m squared minus 3 mn plus 5 n squared close parentheses.\"><\/span><span data-type=\"media\" id=\"fs-id1167834464468\" data-alt=\"Step 4 is to check by multiplying the factors. By multiplying the factors, we get the original polynomial.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_003d_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 4 is to check by multiplying the factors. By multiplying the factors, we get the original polynomial.\"><\/span><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167826996813\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835238831\"><div data-type=\"problem\" id=\"fs-id1167832051959\"><p>Factor: \\(9x{y}^{2}+6{x}^{2}{y}^{2}+21{y}^{3}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835332262\"><p id=\"fs-id1167835368386\">\\(3{y}^{2}\\left(3x+2{x}^{2}+7y\\right)\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167834505596\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167834587406\"><div data-type=\"problem\" id=\"fs-id1167835483550\"><p id=\"fs-id1167835360244\">Factor: \\(3{p}^{3}-6{p}^{2}q+9p{q}^{3}.\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167834505889\">\\(3p\\left({p}^{2}-2pq+3{q}^{2}\\right)\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167832041602\" class=\"howto\"><div data-type=\"title\">Factor the greatest common factor from a polynomial.<\/div><ol id=\"fs-id1167831116496\" type=\"1\" class=\"stepwise\"><li>Find the GCF of all the terms of the polynomial.<\/li><li>Rewrite each term as a product using the GCF.<\/li><li>Use the \u201creverse\u201d Distributive Property to factor the expression.<\/li><li>Check by multiplying the factors.<\/li><\/ol><\/div><div data-type=\"note\" id=\"fs-id1167826967230\"><div data-type=\"title\">Factor as a Noun and a Verb<\/div><p id=\"fs-id1167835264941\">We use \u201cfactor\u201d as both a noun and a verb:<\/p><div data-type=\"equation\" id=\"fs-id1167835335577\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{cccc}\\text{Noun:}\\hfill &amp; &amp; &amp; \\phantom{\\rule{8em}{0ex}}\\text{7 is a}\\phantom{\\rule{0.2em}{0ex}}{\\text{factor}}\\phantom{\\rule{0.2em}{0ex}}\\text{of 14}\\hfill \\\\ \\text{Verb:}\\hfill &amp; &amp; &amp; \\phantom{\\rule{8em}{0ex}}{\\text{factor}}\\phantom{\\rule{0.2em}{0ex}}\\text{3 from}\\phantom{\\rule{0.2em}{0ex}}3a+3\\hfill \\end{array}\\)<\/div><\/div><div data-type=\"example\" id=\"fs-id1167832226526\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167835323694\"><div data-type=\"problem\" id=\"fs-id1167835340040\"><p id=\"fs-id1167835379260\">Factor: \\(5{x}^{3}-25{x}^{2}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834448943\"><table id=\"fs-id1167835355061\" class=\"unnumbered unstyled\" summary=\"First find the GCF of 5 x cubed and 25 x squared. By factoring, bringing down the common factors and multiplying them, we get the GCF as 5 x squared. We rewrite the polynomial as 5 x squared times x minus 5 x squared times 5. Next we factor the GCF and rewrite as 5 x squared open parentheses x minus 5 close parentheses. Finally we check by multiplying the factors to get the original polynomial.\" data-label=\"\"><tbody><tr valign=\"top\"><td colspan=\"2\" data-valign=\"middle\" data-align=\"left\">Find the GCF of \\(5{x}^{3}\\) and \\(25{x}^{2}.\\)<\/td><td data-valign=\"middle\" data-align=\"left\"><span data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_005b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835514387\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_005c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835308604\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_005d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Rewrite each term.<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835258142\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_005e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Factor the GCF.<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_005f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Check:<div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div>\\(\\phantom{\\rule{4em}{0ex}}\\begin{array}{c}\\hfill 5{x}^{2}\\left(x-5\\right)\\hfill \\\\ \\hfill 5{x}^{2}\u00b7x-5{x}^{2}\u00b75\\hfill \\\\ \\hfill 5{x}^{3}-25{x}^{2}\u2713\\hfill \\end{array}\\)<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835335871\" class=\"try\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167834505216\"><p>Factor: \\(2{x}^{3}+12{x}^{2}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834432207\"><p>\\(2{x}^{2}\\left(x+6\\right)\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835347937\" class=\"try\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167832015530\"><p>Factor: \\(6{y}^{3}-15{y}^{2}.\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167834190741\">\\(3{y}^{2}\\left(2y-5\\right)\\)<\/p><\/div><\/div><\/div><div data-type=\"example\" id=\"fs-id1167835370672\" class=\"textbox textbox--examples\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167834193968\"><p id=\"fs-id1167835301394\">Factor: \\(8{x}^{3}y-10{x}^{2}{y}^{2}+12x{y}^{3}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167831825042\"><table id=\"fs-id1167835367729\" class=\"unnumbered unstyled\" summary=\"The GCF of 8 x cubed y minus 10 x squared y squared plus 12 x y cubed is 2xy. Rewriting each term using the GCF, we get 2xy times 4x squared minus 2xy times 5xy plus 2xy times 6 y squared. Factoring out the GCF, we get 2xy open parentheses 4 x squared minus 5xy plus 6 y squared. Finally, we check by multiplying the factors to get the original polynomial.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">The GCF of \\(8{x}^{3}y,-10{x}^{2}{y}^{2},\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}12x{y}^{3}\\)<div data-type=\"newline\"><br><\/div>is \\(2xy.\\)<\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835239981\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_007b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835356022\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_007c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"center\">\u2003\u2003\u2003\u2003\u2003<span data-type=\"media\" id=\"fs-id1167835229282\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_007a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Rewrite each term using the GCF, \\(2xy.\\)\u2003\u2003\u2003\u2003<\/td><td data-valign=\"top\" data-align=\"center\">\u2003\u2003<span data-type=\"media\" id=\"fs-id1167835421099\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_007d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Factor the GCF.<\/td><td data-valign=\"top\" data-align=\"center\">\u2003\u2003\u2003\u2003\u2003<span data-type=\"media\" id=\"fs-id1167830703991\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_007e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Check:<div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div>\\(\\phantom{\\rule{4em}{0ex}}\\begin{array}{c}\\hfill 2xy\\left(4{x}^{2}-5xy+6{y}^{2}\\right)\\hfill \\\\ \\hfill 2xy\u00b74{x}^{2}-2xy\u00b75xy+2xy\u00b76{y}^{2}\\hfill \\\\ \\hfill 8{x}^{3}y-10{x}^{2}{y}^{2}+12x{y}^{3}\u2713\\hfill \\end{array}\\)<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835423184\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835306718\"><div data-type=\"problem\" id=\"fs-id1167835310717\"><p id=\"fs-id1167832058345\">Factor: \\(15{x}^{3}y-3{x}^{2}{y}^{2}+6x{y}^{3}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835362706\"><p id=\"fs-id1167834131221\">\\(3xy\\left(5{x}^{2}-xy+2{y}^{2}\\right)\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167826996512\" class=\"try\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167832152708\"><p id=\"fs-id1167831895303\">Factor: \\(8{a}^{3}b+2{a}^{2}{b}^{2}-6a{b}^{3}.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834196723\"><p>\\(2ab\\left(4{a}^{2}+ab-3{b}^{2}\\right)\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167835327183\">When the leading coefficient is negative, we factor the negative out as part of the GCF.<\/p><div data-type=\"example\" id=\"fs-id1167835346406\" class=\"textbox textbox--examples\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167835262496\"><p id=\"fs-id1167832005973\">Factor: \\(-4{a}^{3}+36{a}^{2}-8a.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834556901\"><p id=\"fs-id1167835330823\">The leading coefficient is negative, so the GCF will be negative.<\/p><table class=\"unnumbered unstyled\" summary=\"We rewrite each term in the polynomial using the GCF minus 4a. So, we get minus 4a times a squared minus open parentheses minus 4 a close parentheses times 9 a plus open parentheses minus 4 a close parentheses times 2. Factoring the GCF, we get minus 4 a open parentheses a squared minus 9a plus 2 close parentheses. Finally, we check by multiplying the factors to get the original polynomial.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"center\"><span data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_008a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Rewrite each term using the GCF, \\(-4a.\\)<\/td><td data-valign=\"top\" data-align=\"center\"><span data-type=\"media\" id=\"fs-id1167835307398\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_008b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Factor the GCF.<\/td><td data-valign=\"top\" data-align=\"center\"><span data-type=\"media\" id=\"fs-id1167832060518\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_008c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Check:<div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div>\\(\\phantom{\\rule{4em}{0ex}}\\begin{array}{c}\\hfill -4a\\left({a}^{2}-9a+2\\right)\\hfill \\\\ \\hfill -4a\u00b7{a}^{2}-\\left(-4a\\right)\u00b79a+\\left(-4a\\right)\u00b72\\hfill \\\\ \\hfill -4{a}^{3}+36{a}^{2}-8a\u2713\\hfill \\end{array}\\)<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835237838\" class=\"try\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167831825025\"><p id=\"fs-id1167831846710\">Factor: \\(-4{b}^{3}+16{b}^{2}-8b.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167832153158\"><p id=\"fs-id1167834395016\">\\(-4b\\left({b}^{2}-4b+2\\right)\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167834423260\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835308305\"><div data-type=\"problem\" id=\"fs-id1167835329145\"><p id=\"fs-id1167835366743\">Factor: \\(-7{a}^{3}+21{a}^{2}-14a.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835341033\"><p id=\"fs-id1167835324798\">\\(-7a\\left({a}^{2}-3a+2\\right)\\)<\/p><\/div><\/div><\/div><p id=\"fs-id1167834252720\">So far our greatest common factors have been monomials. In the next example, the greatest common factor is a binomial.<\/p><div data-type=\"example\" id=\"fs-id1167834308954\" class=\"textbox textbox--examples\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167832055694\"><p>Factor: \\(3y\\left(y+7\\right)-4\\left(y+7\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834061707\"><p id=\"fs-id1167835338725\">The GCF is the binomial \\(y+7.\\)<\/p><table class=\"unnumbered unstyled\" summary=\"The polynomial is 3y open parentheses y plus 7 close parentheses minus 4 open parentheses y plus 7 close parentheses. Factor the GCF open parentheses y plus 7 close parentheses. We get open parentheses y plus 7 close parentheses open parentheses 3y minus 4 close parentheses. Check on your own by multiplying.\" data-label=\"\"><tbody><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\"><\/td><td data-valign=\"top\" data-align=\"center\"><span data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_009a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Factor the GCF, \\(\\left(y+7\\right).\\)<\/td><td data-valign=\"top\" data-align=\"center\"><span data-type=\"media\" id=\"fs-id1167828410744\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_009b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\"><\/span><\/td><\/tr><tr valign=\"top\"><td data-valign=\"top\" data-align=\"left\">Check on your own by multiplying.\u2003\u2003\u2003<\/td><td data-valign=\"top\" data-align=\"left\"><\/td><\/tr><\/tbody><\/table><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835329782\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167834472269\"><div data-type=\"problem\" id=\"fs-id1167835349236\"><p>Factor: \\(4m\\left(m+3\\right)-7\\left(m+3\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835307821\"><p id=\"fs-id1167826994245\">\\(\\left(m+3\\right)\\left(4m-7\\right)\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" class=\"try\"><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167831116851\"><p id=\"fs-id1167834133021\">Factor: \\(8n\\left(n-4\\right)+5\\left(n-4\\right).\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834537857\"><p>\\(\\left(n-4\\right)\\left(8n+5\\right)\\)<\/p><\/div><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167834438900\"><h3 data-type=\"title\">Factor by Grouping<\/h3><p id=\"fs-id1167835340140\">Sometimes there is no common factor of all the terms of a polynomial. When there are four terms we separate the polynomial into two parts with two terms in each part. Then look for the <span data-type=\"term\" class=\"no-emphasis\">GCF<\/span> in each part. If the polynomial can be factored, you will find a common factor emerges from both parts. Not all polynomials can be factored. Just like some numbers are <span data-type=\"term\" class=\"no-emphasis\">prime<\/span>, some polynomials are prime.<\/p><div data-type=\"example\" class=\"textbox textbox--examples\"><div data-type=\"title\">How to Factor a Polynomial by Grouping<\/div><div data-type=\"exercise\" id=\"fs-id1167835594921\"><div data-type=\"problem\" id=\"fs-id1167832041513\"><p>Factor by grouping: \\(xy+3y+2x+6.\\)<\/p><\/div><div data-type=\"solution\"><span data-type=\"media\" data-alt=\"Step 1 is to group the terms with common factors. There is no greatest common factor in all the four terms of xy plus 3y plus 2x plus 6. So, separate the first two terms from the second two.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_010a_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is to group the terms with common factors. There is no greatest common factor in all the four terms of xy plus 3y plus 2x plus 6. So, separate the first two terms from the second two.\"><\/span><span data-type=\"media\" id=\"fs-id1167835345071\" data-alt=\"Step 2 is to factor out the common factor in each group. By factoring the GCF from the first 2 terms, we get y open parentheses x plus 3 close parentheses plus 2x plus 6. Factoring the GCF from the second 2 terms, we get y open parentheses x plus 3 close parentheses plus 2 open parentheses x plus 3 close parentheses.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_010b_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 2 is to factor out the common factor in each group. By factoring the GCF from the first 2 terms, we get y open parentheses x plus 3 close parentheses plus 2x plus 6. Factoring the GCF from the second 2 terms, we get y open parentheses x plus 3 close parentheses plus 2 open parentheses x plus 3 close parentheses.\"><\/span><span data-type=\"media\" id=\"fs-id1167835190796\" data-alt=\"Step 3 is to factor the common factor from the expression. Notice that each term has a common factor of x plus 3. By factoring this out, we get open parentheses x plus 3 close parentheses open parentheses y plus 2 close parentheses\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_010c_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 3 is to factor the common factor from the expression. Notice that each term has a common factor of x plus 3. By factoring this out, we get open parentheses x plus 3 close parentheses open parentheses y plus 2 close parentheses\"><\/span><span data-type=\"media\" data-alt=\"Step 4 is to check by multiplying the expressions to get the result xy plus 3y plus 2x plus 6.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_010d_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 4 is to check by multiplying the expressions to get the result xy plus 3y plus 2x plus 6.\"><\/span><\/div><\/div><\/div><div data-type=\"note\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835305027\"><div data-type=\"problem\"><p>Factor by grouping: \\(xy+8y+3x+24.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835339253\"><p>\\(\\left(x+8\\right)\\left(y+3\\right)\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167832060644\" class=\"try\"><div data-type=\"exercise\"><div data-type=\"problem\"><p id=\"fs-id1167834515926\">Factor by grouping: \\(ab+7b+8a+56.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835464002\"><p id=\"fs-id1167835188009\">\\(\\left(a+7\\right)\\left(b+8\\right)\\)<\/p><\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835187158\" class=\"howto\"><div data-type=\"title\">Factor by grouping.<\/div><ol id=\"fs-id1167835308131\" type=\"1\" class=\"stepwise\"><li>Group terms with common factors.<\/li><li>Factor out the common factor in each group.<\/li><li>Factor the common factor from the expression.<\/li><li>Check by multiplying the factors.<\/li><\/ol><\/div><div data-type=\"example\" id=\"fs-id1167835321886\" class=\"textbox textbox--examples\"><div data-type=\"exercise\" id=\"fs-id1167831919943\"><div data-type=\"problem\"><p id=\"fs-id1167832195761\">Factor by grouping: <span class=\"token\">\u24d0<\/span> \\({x}^{2}+3x-2x-6\\) <span class=\"token\">\u24d1<\/span> \\(6{x}^{2}-3x-4x+2.\\)<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167835325203\"><span class=\"token\">\u24d0<\/span><\/p><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{cccccc}\\text{There is no GCF in all four terms.}\\hfill &amp; &amp; &amp; &amp; &amp; {x}^{2}+3x-2x-6\\hfill \\\\ \\text{Separate into two parts.}\\hfill &amp; &amp; &amp; &amp; &amp; {x}^{2}+3x\\phantom{\\rule{1.5em}{0ex}}-2x-6\\hfill \\\\ \\begin{array}{c}\\text{Factor the GCF from both parts. Be careful}\\hfill \\\\ \\text{with the signs when factoring the GCF from}\\hfill \\\\ \\text{the last two terms.}\\hfill \\end{array}\\hfill &amp; &amp; &amp; &amp; &amp; x\\left(x+3\\right)-2\\left(x+3\\right)\\hfill \\\\ \\text{Factor out the common factor.}\\hfill &amp; &amp; &amp; &amp; &amp; \\left(x+3\\right)\\left(x-2\\right)\\hfill \\\\ \\text{Check on your own by multiplying.}\\hfill &amp; &amp; &amp; &amp; &amp; \\end{array}\\)<div data-type=\"newline\"><br><\/div><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span><div data-type=\"newline\"><br><\/div>\\(\\begin{array}{cccccc}\\text{There is no GCF in all four terms.}\\hfill &amp; &amp; &amp; &amp; &amp; \\phantom{\\rule{3em}{0ex}}6{x}^{2}-3x-4x+2\\hfill \\\\ \\text{Separate into two parts.}\\hfill &amp; &amp; &amp; &amp; &amp; \\phantom{\\rule{3em}{0ex}}6{x}^{2}-3x\\phantom{\\rule{1.5em}{0ex}}-4x+2\\hfill \\\\ \\text{Factor the GCF from both parts.}\\hfill &amp; &amp; &amp; &amp; &amp; \\phantom{\\rule{3em}{0ex}}3x\\left(2x-1\\right)-2\\left(2x-1\\right)\\hfill \\\\ \\text{Factor out the common factor.}\\hfill &amp; &amp; &amp; &amp; &amp; \\phantom{\\rule{3em}{0ex}}\\left(2x-1\\right)\\left(3x-2\\right)\\hfill \\\\ \\text{Check on your own by multiplying.}\\hfill &amp; &amp; &amp; &amp; &amp; \\end{array}\\)<\/div><\/div><\/div><div data-type=\"note\" id=\"fs-id1167835268015\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167835299941\"><div data-type=\"problem\" id=\"fs-id1167835585149\"><p>Factor by grouping: <span class=\"token\">\u24d0<\/span> \\({x}^{2}+2x-5x-10\\) <span class=\"token\">\u24d1<\/span> \\(20{x}^{2}-16x-15x+12.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834183816\"><p id=\"fs-id1167835595339\"><span class=\"token\">\u24d0<\/span>\\(\\left(x-5\\right)\\left(x+2\\right)\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(\\left(5x-4\\right)\\left(4x-3\\right)\\)<\/div><\/div><\/div><div data-type=\"note\" class=\"try\"><div data-type=\"exercise\" id=\"fs-id1167826814135\"><div data-type=\"problem\" id=\"fs-id1167834430060\"><p id=\"fs-id1167826803903\">Factor by grouping: <span class=\"token\">\u24d0<\/span> \\({y}^{2}+4y-7y-28\\) <span class=\"token\">\u24d1<\/span> \\(42{m}^{2}-18m-35m+15.\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167828410732\"><p id=\"fs-id1167835202851\"><span class=\"token\">\u24d0<\/span>\\(\\left(y+4\\right)\\left(y-7\\right)\\)<\/p><div data-type=\"newline\"><br><\/div><span class=\"token\">\u24d1<\/span>\\(\\left(7m-3\\right)\\left(6m-5\\right)\\)<\/div><\/div><\/div><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167831923591\"><h3 data-type=\"title\">Key Concepts<\/h3><ul id=\"fs-id1167834433471\" data-bullet-style=\"bullet\"><li><strong data-effect=\"bold\">How to find the greatest common factor (GCF) of two expressions.<\/strong><ol id=\"fs-id1167827987881\" type=\"1\" class=\"stepwise\"><li>Factor each coefficient into primes. Write all variables with exponents in expanded form.<\/li><li>List all factors\u2014matching common factors in a column. In each column, circle the common factors.<\/li><li>Bring down the common factors that all expressions share.<\/li><li>Multiply the factors.<\/li><\/ol><\/li><li><strong data-effect=\"bold\">Distributive Property:<\/strong> If <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em> are real numbers, then<div data-type=\"newline\"><br><\/div> <div data-type=\"equation\" id=\"fs-id1167831835907\" class=\"unnumbered\" data-label=\"\">\\(a\\left(b+c\\right)=ab+ac\\phantom{\\rule{1em}{0ex}}\\text{and}\\phantom{\\rule{1em}{0ex}}ab+ac=a\\left(b+c\\right)\\)<\/div><div data-type=\"newline\"><br><\/div> The form on the left is used to multiply. The form on the right is used to factor.<\/li><li><strong data-effect=\"bold\">How to factor the greatest common factor from a polynomial.<\/strong><ol id=\"fs-id1167832054265\" type=\"1\" class=\"stepwise\"><li>Find the GCF of all the terms of the polynomial.<\/li><li>Rewrite each term as a product using the GCF.<\/li><li>Use the \u201creverse\u201d Distributive Property to factor the expression.<\/li><li>Check by multiplying the factors.<\/li><\/ol><\/li><li><strong data-effect=\"bold\">Factor as a Noun and a Verb:<\/strong> We use \u201cfactor\u201d as both a noun and a verb.<div data-type=\"newline\"><br><\/div> <div data-type=\"equation\" id=\"fs-id1167831116300\" class=\"unnumbered\" data-label=\"\">\\(\\begin{array}{cccc}\\text{Noun:}\\hfill &amp; &amp; &amp; \\text{7 is a}\\phantom{\\rule{0.2em}{0ex}}{\\text{factor}}\\phantom{\\rule{0.2em}{0ex}}\\text{of 14}\\hfill \\\\ \\text{Verb:}\\hfill &amp; &amp; &amp; {\\text{factor}}\\phantom{\\rule{0.2em}{0ex}}\\text{3 from}\\phantom{\\rule{0.2em}{0ex}}3a+3\\hfill \\end{array}\\)<\/div><\/li><li><strong data-effect=\"bold\">How to factor by grouping.<\/strong><ol id=\"fs-id1167826801698\" type=\"1\" class=\"stepwise\"><li>Group terms with common factors.<\/li><li>Factor out the common factor in each group.<\/li><li>Factor the common factor from the expression.<\/li><li>Check by multiplying the factors.<\/li><\/ol><\/li><\/ul><\/div><div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167835215319\"><div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1167834308203\"><h4 data-type=\"title\">Practice Makes Perfect<\/h4><p id=\"fs-id1167835307743\"><strong data-effect=\"bold\">Find the Greatest Common Factor of Two or More Expressions<\/strong><\/p><p id=\"fs-id1167835336534\">In the following exercises, find the greatest common factor.<\/p><div data-type=\"exercise\" id=\"fs-id1167831890415\"><div data-type=\"problem\" id=\"fs-id1167834556665\"><p id=\"fs-id1167834403274\">\\(10{p}^{3}q,12p{q}^{2}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835337582\"><p id=\"fs-id1167830868646\">\\(2pq\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834065925\"><div data-type=\"problem\" id=\"fs-id1167831883509\"><p id=\"fs-id1167835333240\">\\(8{a}^{2}{b}^{3},10a{b}^{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832059919\"><div data-type=\"problem\" id=\"fs-id1167832133982\"><p id=\"fs-id1167835237682\">\\(12{m}^{2}{n}^{3},30{m}^{5}{n}^{3}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835173235\"><p id=\"fs-id1167835235925\">\\(6{m}^{2}{n}^{3}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835186941\"><div data-type=\"problem\" id=\"fs-id1167834239042\"><p id=\"fs-id1167831116606\">\\(28{x}^{2}{y}^{4},42{x}^{4}{y}^{4}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835349597\"><div data-type=\"problem\" id=\"fs-id1167835306791\"><p id=\"fs-id1167835374776\">\\(10{a}^{3},12{a}^{2},14a\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835419990\"><p id=\"fs-id1167835418113\">\\(2a\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835421936\"><div data-type=\"problem\" id=\"fs-id1167834538766\"><p id=\"fs-id1167835423323\">\\(20{y}^{3},28{y}^{2},40y\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835187200\"><div data-type=\"problem\" id=\"fs-id1167831871864\"><p id=\"fs-id1167834064707\">\\(35{x}^{3}{y}^{2},10{x}^{4}y,5{x}^{5}{y}^{3}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834156917\"><p id=\"fs-id1167832075976\">\\(5{x}^{3}y\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835380762\"><div data-type=\"problem\" id=\"fs-id1167832036187\"><p id=\"fs-id1167834357146\">\\(27{p}^{2}{q}^{3},45{p}^{3}{q}^{4},9{p}^{4}{q}^{3}\\)<\/p><\/div><\/div><p id=\"fs-id1167835380474\"><strong data-effect=\"bold\">Factor the Greatest Common Factor from a Polynomial<\/strong><\/p><p id=\"fs-id1167834062656\">In the following exercises, factor the greatest common factor from each polynomial.<\/p><div data-type=\"exercise\" id=\"fs-id1167835321212\"><div data-type=\"problem\" id=\"fs-id1167834097776\"><p id=\"fs-id1167831117445\">\\(6m+9\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834403394\"><p id=\"fs-id1167834246589\">\\(3\\left(2m+3\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167830697830\"><div data-type=\"problem\" id=\"fs-id1167835191989\"><p id=\"fs-id1167834191594\">\\(14p+35\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167831883792\"><div data-type=\"problem\" id=\"fs-id1167835328863\"><p id=\"fs-id1167835229373\">\\(9n-63\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167830693436\"><p id=\"fs-id1167831883382\">\\(9\\left(n-7\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835381410\"><div data-type=\"problem\" id=\"fs-id1167835230324\"><p id=\"fs-id1167834403298\">\\(45b-18\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834192385\"><div data-type=\"problem\" id=\"fs-id1167835421055\"><p id=\"fs-id1167835233290\">\\(3{x}^{2}+6x-9\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835363865\"><p id=\"fs-id1167835301588\">\\(3\\left({x}^{2}+2x-3\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834185484\"><div data-type=\"problem\" id=\"fs-id1167835513601\"><p id=\"fs-id1167835358548\">\\(4{y}^{2}+8y-4\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832043698\"><div data-type=\"problem\" id=\"fs-id1167834219471\"><p id=\"fs-id1167835310143\">\\(8{p}^{2}+4p+2\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167828447183\"><p id=\"fs-id1167826978899\">\\(2\\left(4{p}^{2}+2p+1\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167828421716\"><div data-type=\"problem\" id=\"fs-id1167831040276\"><p id=\"fs-id1167835389992\">\\(10{q}^{2}+14q+20\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832042721\"><div data-type=\"problem\" id=\"fs-id1167834462857\"><p id=\"fs-id1167826993902\">\\(8{y}^{3}+16{y}^{2}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167831883492\"><p id=\"fs-id1167831922684\">\\(8{y}^{2}\\left(y+2\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835629180\"><div data-type=\"problem\" id=\"fs-id1167834464406\"><p id=\"fs-id1167832151513\">\\(12{x}^{3}-10x\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835483676\"><div data-type=\"problem\" id=\"fs-id1167834280064\"><p id=\"fs-id1167834194415\">\\(5{x}^{3}-15{x}^{2}+20x\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835351982\"><p id=\"fs-id1167831890778\">\\(5x\\left({x}^{2}-3x+4\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167831880194\"><div data-type=\"problem\" id=\"fs-id1167832041560\"><p id=\"fs-id1167834555206\">\\(8{m}^{2}-40m+16\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832053525\"><div data-type=\"problem\" id=\"fs-id1167835233897\"><p id=\"fs-id1167830963422\">\\(24{x}^{3}-12{x}^{2}+15x\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167826808708\"><p>\\(3x\\left(8{x}^{2}-4x+5\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835233120\"><div data-type=\"problem\" id=\"fs-id1167835231120\"><p id=\"fs-id1167835301823\">\\(24{y}^{3}-18{y}^{2}-30y\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835514026\"><div data-type=\"problem\" id=\"fs-id1167835513221\"><p id=\"fs-id1167834556053\">\\(12x{y}^{2}+18{x}^{2}{y}^{2}-30{y}^{3}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167831920308\"><p id=\"fs-id1167832051769\">\\(6{y}^{2}\\left(2x+3{x}^{2}-5y\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834505039\"><div data-type=\"problem\" id=\"fs-id1167834396469\"><p id=\"fs-id1167834506190\">\\(21p{q}^{2}+35{p}^{2}{q}^{2}-28{q}^{3}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835327156\"><div data-type=\"problem\" id=\"fs-id1167835362634\"><p id=\"fs-id1167834053526\">\\(20{x}^{3}y-4{x}^{2}{y}^{2}+12x{y}^{3}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834463054\"><p id=\"fs-id1167834463056\">\\(4xy\\left(5{x}^{2}-xy+3{y}^{2}\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834395336\"><div data-type=\"problem\" id=\"fs-id1167834395338\"><p id=\"fs-id1167831910118\">\\(24{a}^{3}b+6{a}^{2}{b}^{2}-18a{b}^{3}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826995349\"><div data-type=\"problem\" id=\"fs-id1167835236135\"><p id=\"fs-id1167835236137\">\\(-2x-4\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835303487\"><p id=\"fs-id1167835303489\">\\(-2\\left(x+4\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834289446\"><div data-type=\"problem\" id=\"fs-id1167835387157\"><p id=\"fs-id1167835387159\">\\(-3b+12\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835416377\"><div data-type=\"problem\" id=\"fs-id1167832226484\"><p id=\"fs-id1167832226486\">\\(-2{x}^{3}+18{x}^{2}-8x\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834300326\"><p id=\"fs-id1167831847191\">\\(-2x\\left({x}^{2}-9x+4\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832058680\"><div data-type=\"problem\" id=\"fs-id1167834185856\"><p id=\"fs-id1167834079542\">\\(-5{y}^{3}+35{y}^{2}-15y\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835417781\"><div data-type=\"problem\" id=\"fs-id1167835417783\"><p id=\"fs-id1167834300625\">\\(-4{p}^{3}q-12{p}^{2}{q}^{2}+16p{q}^{2}\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835422237\"><p id=\"fs-id1167834060402\">\\(-4pq\\left({p}^{2}+3pq-4q\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835310781\"><div data-type=\"problem\" id=\"fs-id1167835311413\"><p id=\"fs-id1167835311415\">\\(-6{a}^{3}b-12{a}^{2}{b}^{2}+18a{b}^{2}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835337185\"><div data-type=\"problem\" id=\"fs-id1167835213524\"><p id=\"fs-id1167834229188\">\\(5x\\left(x+1\\right)+3\\left(x+1\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167831890913\"><p id=\"fs-id1167826814057\">\\(\\left(x+1\\right)\\left(5x+3\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834120568\"><div data-type=\"problem\" id=\"fs-id1167834120570\"><p id=\"fs-id1167827988062\">\\(2x\\left(x-1\\right)+\\phantom{\\rule{0.2em}{0ex}}9\\left(x-1\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835381458\"><div data-type=\"problem\" id=\"fs-id1167835381460\"><p id=\"fs-id1167835319923\">\\(3b\\left(b-2\\right)-13\\left(b-2\\right)\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834429474\"><p id=\"fs-id1167835410518\">\\(\\left(b-2\\right)\\left(3b-13\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167827967167\"><div data-type=\"problem\" id=\"fs-id1167827967169\"><p id=\"fs-id1167835503992\">\\(6m\\left(m-5\\right)-7\\left(m-5\\right)\\)<\/p><\/div><\/div><p id=\"fs-id1167835367819\"><strong data-effect=\"bold\">Factor by Grouping<\/strong><\/p><p id=\"fs-id1167826966819\">In the following exercises, factor by grouping.<\/p><div data-type=\"exercise\" id=\"fs-id1167826966822\"><div data-type=\"problem\" id=\"fs-id1167835353655\"><p>\\(ab+5a+3b+15\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167830964376\"><p id=\"fs-id1167830964378\">\\(\\left(b+5\\right)\\left(a+3\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834583319\"><div data-type=\"problem\" id=\"fs-id1167834583321\"><p id=\"fs-id1167834562482\">\\(cd+6c+4d+24\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167831824322\"><div data-type=\"problem\" id=\"fs-id1167831824324\"><p id=\"fs-id1167835306581\">\\(8{y}^{2}+y+40y+5\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167827988156\"><p id=\"fs-id1167835355764\">\\(\\left(y+5\\right)\\left(8y+1\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835609625\"><div data-type=\"problem\" id=\"fs-id1167835609627\"><p id=\"fs-id1167826857108\">\\(6{y}^{2}+7y+24y+28\\)<\/p><\/div><\/div><div data-type=\"exercise\"><div data-type=\"problem\" id=\"fs-id1167830704254\"><p id=\"fs-id1167830704256\">\\(uv-9u+2v-18\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835365743\"><p>\\(\\left(u+2\\right)\\left(v-9\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835288046\"><div data-type=\"problem\" id=\"fs-id1167835288049\"><p id=\"fs-id1167834430816\">\\(pq-10p+8q-80\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167830702860\"><div data-type=\"problem\" id=\"fs-id1167830702862\"><p id=\"fs-id1167830960717\">\\({u}^{2}-u+6u-6\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835483711\"><p id=\"fs-id1167835483713\">\\(\\left(u-1\\right)\\left(u+6\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167827957103\"><div data-type=\"problem\" id=\"fs-id1167827957105\"><p id=\"fs-id1167831106969\">\\({x}^{2}-x+4x-4\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835420263\"><div data-type=\"problem\" id=\"fs-id1167835420266\"><p id=\"fs-id1167834473406\">\\(9{p}^{2}-3p-20\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834556761\"><p id=\"fs-id1167834472577\">\\(\\left(3p-5\\right)\\left(3p+4\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835279990\"><div data-type=\"problem\" id=\"fs-id1167834463003\"><p id=\"fs-id1167834463006\">\\(16{q}^{2}-8q-35\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826801811\"><div data-type=\"problem\" id=\"fs-id1167826801814\"><p id=\"fs-id1167826997425\">\\(mn-6m-4n+24\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167831881876\"><p id=\"fs-id1167831959287\">\\(\\left(n-6\\right)\\left(m-4\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167832067463\"><div data-type=\"problem\" id=\"fs-id1167830838248\"><p id=\"fs-id1167830838250\">\\({r}^{2}-3r-r+3\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835307679\"><div data-type=\"problem\" id=\"fs-id1167835305778\"><p id=\"fs-id1167835305780\">\\(2{x}^{2}-14x-5x+35\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835370068\"><p id=\"fs-id1167834094604\">\\(\\left(x-7\\right)\\left(2x-5\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835309245\"><div data-type=\"problem\" id=\"fs-id1167835309247\"><p id=\"fs-id1167834464434\">\\(4{x}^{2}-36x-3x+27\\)<\/p><\/div><\/div><p id=\"fs-id1167834120191\"><strong data-effect=\"bold\">Mixed Practice<\/strong><\/p><p id=\"fs-id1167835319069\">In the following exercises, factor.<\/p><div data-type=\"exercise\" id=\"fs-id1167834516217\"><div data-type=\"problem\"><p>\\(-18x{y}^{2}-27{x}^{2}y\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835360501\"><p id=\"fs-id1167832058205\">\\(-9xy\\left(3x+2y\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835352834\"><div data-type=\"problem\" id=\"fs-id1167835352836\"><p id=\"fs-id1167834228318\">\\(-4{x}^{3}{y}^{5}-{x}^{2}{y}^{3}+12x{y}^{4}\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167826802847\"><div data-type=\"problem\" id=\"fs-id1167835330068\"><p id=\"fs-id1167835330070\">\\(3{x}^{3}-7{x}^{2}+6x-14\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167834501736\"><p id=\"fs-id1167834501738\">\\(\\left({x}^{2}+2\\right)\\left(3x-7\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\"><div data-type=\"problem\"><p id=\"fs-id1167831881339\">\\({x}^{3}+{x}^{2}-x-1\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835365610\"><div data-type=\"problem\" id=\"fs-id1167835363965\"><p id=\"fs-id1167835363967\">\\({x}^{2}+xy+5x+5y\\)<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167835311280\"><p id=\"fs-id1167835358348\">\\(\\left(x+y\\right)\\left(x+5\\right)\\)<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167835304678\"><div data-type=\"problem\" id=\"fs-id1167835304680\"><p id=\"fs-id1167835304683\">\\(5{x}^{3}-3{x}^{2}+5x-3\\)<\/p><\/div><\/div><\/div><div class=\"writing\" data-depth=\"2\" id=\"fs-id1167834095298\"><h4 data-type=\"title\">Writing Exercises<\/h4><div data-type=\"exercise\" id=\"fs-id1167834535535\"><div data-type=\"problem\" id=\"fs-id1167835239421\"><p id=\"fs-id1167835239423\">What does it mean to say a polynomial is in factored form?<\/p><\/div><div data-type=\"solution\"><p id=\"fs-id1167835368947\">Answers will vary.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167828420166\"><div data-type=\"problem\" id=\"fs-id1167835585152\"><p id=\"fs-id1167835585154\">How do you check result after factoring a polynomial?<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167831985770\"><div data-type=\"problem\" id=\"fs-id1167831911253\"><p id=\"fs-id1167831911255\">The greatest common factor of 36 and 60 is 12. Explain what this means.<\/p><\/div><div data-type=\"solution\" id=\"fs-id1167828420268\"><p id=\"fs-id1167828420270\">Answers will vary.<\/p><\/div><\/div><div data-type=\"exercise\" id=\"fs-id1167834131452\"><div data-type=\"problem\" id=\"fs-id1167832138624\"><p id=\"fs-id1167832138626\">What is the GCF of \\({y}^{4},{y}^{5},\\) and \\({y}^{10}?\\) Write a general rule that tells you how to find the GCF of \\({y}^{a},{y}^{b},\\) and \\({y}^{c}.\\)<\/p><\/div><\/div><\/div><div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167834552513\"><h4 data-type=\"title\">Self Check<\/h4><p><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p><span data-type=\"media\" id=\"fs-id1167835514036\" data-alt=\"This table has 4 columns, 3 rows and a header row. The header row labels each column I can, confidently, with some help and no I don\u2019t get it. The first column has the following statements: find the greatest common factor of 2 or more expressions, factor the greatest common factor from a polynomial, factor by grouping. The remaining columns are blank.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_201_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This table has 4 columns, 3 rows and a header row. The header row labels each column I can, confidently, with some help and no I don\u2019t get it. The first column has the following statements: find the greatest common factor of 2 or more expressions, factor the greatest common factor from a polynomial, factor by grouping. The remaining columns are blank.\"><\/span><p id=\"fs-id1167831835712\"><span class=\"token\">\u24d1<\/span> If most of your checks were:<\/p><p id=\"fs-id1167830960474\"><strong data-effect=\"bold\">\u2026confidently.<\/strong> Congratulations! You have achieved your goals in this section! Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific!<\/p><p id=\"fs-id1167835360981\"><strong data-effect=\"bold\">\u2026with some help.<\/strong> This must be addressed quickly as topics you do not master become potholes in your road to success. Math is sequential - every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?<\/p><p id=\"fs-id1167835352370\"><strong data-effect=\"bold\">\u2026no - I don\u2019t get it!<\/strong> This is critical and you must not ignore it. You need to get help immediately or you will quickly be overwhelmed. See your instructor as soon as possible to discuss your situation. Together you can come up with a plan to get you the help you need.<\/p><\/div><\/div><div data-type=\"glossary\" class=\"textbox shaded\"><h3 data-type=\"glossary-title\">Glossary<\/h3><dl id=\"fs-id1167835371075\"><dt>factoring<\/dt><dd id=\"fs-id1167835371080\">Splitting a product into factors is called factoring.<\/dd><\/dl><dl id=\"fs-id1167834535267\"><dt>greatest common factor<\/dt><dd id=\"fs-id1167834346320\">The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.<\/dd><\/dl><\/div>\n","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to: <\/p>\n<ul>\n<li>Find the greatest common factor of two or more expressions<\/li>\n<li>Factor the greatest common factor from a polynomial<\/li>\n<li>Factor by grouping<\/li>\n<\/ul>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835305786\" class=\"be-prepared\">\n<p id=\"fs-id1167835420924\">Before you get started, take this readiness quiz.<\/p>\n<ol id=\"fs-id1167835236318\" type=\"1\">\n<li>Factor 56 into primes.\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167829937177\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>Find the least common multiple (LCM) of 18 and 24.\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/d3697553-3900-453f-8c08-8f74d55711ba#fs-id1167829937221\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<li>Multiply: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f8906fb3f7c9b17b00f7347020f275ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#97;&#43;&#56;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"111\" style=\"vertical-align: -4px;\" \/>\n<div data-type=\"newline\"><\/div>\n<p> If you missed this problem, review <a href=\"\/contents\/0b9be1db-21c4-4bd0-8f8e-d809f6ff7c8c#fs-id1167829810683\" class=\"autogenerated-content\">(Figure)<\/a>.<\/li>\n<\/ol>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167832153812\">\n<h3 data-type=\"title\">Find the Greatest Common Factor of Two or More Expressions<\/h3>\n<p id=\"fs-id1167835380264\">Earlier we multiplied factors together to get a <span data-type=\"term\" class=\"no-emphasis\">product<\/span>. Now, we will reverse this process; we will start with a product and then break it down into its factors. Splitting a product into factors is called <span data-type=\"term\">factoring<\/span>.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167834228697\" data-alt=\"8 times 7 is 56. Here 8 and 7 are factors and 56 is the product. An arrow pointing from 8 times 7 to 56 is labeled multiply. An arrow pointing from 56 to 8 times 7 is labeled factor. 2x open parentheses x plus 3 close parentheses equals 2x squared plus 6x. Here the left side of the equation is labeled factors and the right side is labeled products.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_001_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"8 times 7 is 56. Here 8 and 7 are factors and 56 is the product. An arrow pointing from 8 times 7 to 56 is labeled multiply. An arrow pointing from 56 to 8 times 7 is labeled factor. 2x open parentheses x plus 3 close parentheses equals 2x squared plus 6x. Here the left side of the equation is labeled factors and the right side is labeled products.\" \/><\/span><\/p>\n<p id=\"fs-id1167835339323\">We have learned how to factor numbers to find the least common multiple (LCM) of two or more numbers. Now we will factor expressions and find the <span data-type=\"term\">greatest common factor<\/span> of two or more expressions. The method we use is similar to what we used to find the LCM.<\/p>\n<div data-type=\"note\" id=\"fs-id1167834092857\">\n<div data-type=\"title\">Greatest Common Factor<\/div>\n<p id=\"fs-id1167834195947\">The <strong data-effect=\"bold\">greatest common factor<\/strong> (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.<\/p>\n<\/div>\n<p id=\"fs-id1167834284447\">We summarize the steps we use to find the greatest common factor.<\/p>\n<div data-type=\"note\" id=\"fs-id1167832065589\" class=\"howto\">\n<div data-type=\"title\">Find the greatest common factor (GCF) of two expressions.<\/div>\n<ol id=\"fs-id1167835377721\" type=\"1\" class=\"stepwise\">\n<li>Factor each coefficient into primes. Write all variables with exponents in expanded form.<\/li>\n<li>List all factors\u2014matching common factors in a column. In each column, circle the common factors.<\/li>\n<li>Bring down the common factors that all expressions share.<\/li>\n<li>Multiply the factors.<\/li>\n<\/ol>\n<\/div>\n<p id=\"fs-id1167826782766\">The next example will show us the steps to find the greatest common factor of three expressions.<\/p>\n<div data-type=\"example\" id=\"fs-id1167835345627\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167826864261\">\n<div data-type=\"problem\" id=\"fs-id1167835304441\">\n<p id=\"fs-id1167835328287\">Find the greatest common factor of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1a4461f01962efb842c840f65ced6948_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#44;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#53;&#120;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834111768\">\n<table id=\"fs-id1167832056779\" class=\"unnumbered unstyled\" summary=\"The terms are 21 x cubed, 9 x squared and 15 x. The first step is to factor each coefficient into primes and write the variables with exponents in expanded form. 21 x cubed is written as 3 times 7 times x times x times x. 9 x squared is written as 3 times 3 times x times x. 15 x is written as 3 times 5 times x. Now bring down the common factors. So, GCF is 3 times x. Now multiply the factors. So, GCF of 21 x cubed, 9 x squared and 15x is 3x.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Factor each coefficient into primes and write the<\/p>\n<div data-type=\"newline\"><\/div>\n<p>variables with exponents in expanded form.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Circle the common factors in each column.<\/p>\n<div data-type=\"newline\"><\/div>\n<p>Bring down the common factors.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835198732\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_002a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Multiply the factors.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167826927120\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_002b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\">The GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-1fd6c3f6114fa33cb3d4f11ed2cbdbde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"35\" style=\"vertical-align: -1px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b1b5fd89b5219b9297f899b52acb9e4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-15280d18608293c164f1ad95092a47c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"27\" style=\"vertical-align: -1px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bcea841b93e6d1c6150bf94b4036ab3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167834432356\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167830838256\">\n<div data-type=\"problem\" id=\"fs-id1167834196401\">\n<p id=\"fs-id1167831910334\">Find the greatest common factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-32ae431ee4410ab469c73bcbe6215544_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#44;&#51;&#53;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#44;&#50;&#48;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"143\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834538418\">\n<p id=\"fs-id1167835214252\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-73d70cc15de8dab880a6427ad70ed4f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#109;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"32\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167834510590\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167831112380\">\n<div data-type=\"problem\" id=\"fs-id1167835331913\">\n<p>Find the greatest common factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-52b4a55997a2b8ff0af744d55f1fcbfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#44;&#55;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#48;&#53;&#120;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"127\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835341858\">\n<p id=\"fs-id1167835368345\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-21c22354b95d8047439895fca18899e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"19\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167834124439\">\n<h3 data-type=\"title\">Factor the Greatest Common Factor from a Polynomial<\/h3>\n<p id=\"fs-id1167835421146\">It is sometimes useful to represent a number as a product of factors, for example, 12 as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-77bb6dd391aeb20b45faaa418fa77b4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&middot;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ec9f12470dc04e59538f03cd81aa5864_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&middot;&#52;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> In algebra, it can also be useful to represent a polynomial in factored form. We will start with a product, such as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e966c34e11fa21e9f3d9e46779c103a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#53;&#120;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -4px;\" \/> and end with its factors, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5d46139c3bae55e8057af50c8f92f6c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"83\" style=\"vertical-align: -4px;\" \/> To do this we apply the Distributive Property \u201cin reverse.\u201d<\/p>\n<p id=\"fs-id1167835304585\">We state the Distributive Property here just as you saw it in earlier chapters and \u201cin reverse.\u201d<\/p>\n<div data-type=\"note\" id=\"fs-id1167835216215\">\n<div data-type=\"title\">Distributive Property<\/div>\n<p id=\"fs-id1167832195752\">If <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em> are real numbers, then<\/p>\n<div data-type=\"equation\" id=\"fs-id1167832054886\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9dc3219c7fceb55c81eca5b3049cd20b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#97;&#98;&#43;&#97;&#99;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#98;&#43;&#97;&#99;&#61;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"348\" style=\"vertical-align: -4px;\" \/><\/div>\n<p id=\"fs-id1167834279599\">The form on the left is used to multiply. The form on the right is used to factor.<\/p>\n<\/div>\n<p>So how do you use the Distributive Property to factor a <span data-type=\"term\" class=\"no-emphasis\">polynomial<\/span>? You just find the GCF of all the terms and write the polynomial as a product!<\/p>\n<div data-type=\"example\" id=\"fs-id1167835380170\" class=\"textbox textbox--examples\">\n<div data-type=\"title\">How to Use the Distributive Property to factor a polynomial<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826994118\">\n<div data-type=\"problem\" id=\"fs-id1167835214077\">\n<p id=\"fs-id1167834516153\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b1ae57da9096517c8138670b47ab98e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#110;&#43;&#50;&#48;&#109;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"183\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834494820\"><span data-type=\"media\" id=\"fs-id1167831920033\" data-alt=\"Step 1 is find the GCF of all the terms in the polynomial. GCF of 8 m cubed, 12 m squared n and 20 mn squared is 4m.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_003a_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is find the GCF of all the terms in the polynomial. GCF of 8 m cubed, 12 m squared n and 20 mn squared is 4m.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167835280158\" data-alt=\"Step 1 is find the GCF of all the terms in the polynomial. GCF of 8 m cubed, 12 m squared n and 20 mn squared is 4m.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_003b_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is find the GCF of all the terms in the polynomial. GCF of 8 m cubed, 12 m squared n and 20 mn squared is 4m.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167832046576\" data-alt=\"In step 3, use the reverse Distributive Property to factor the expression as 4m open parentheses 2 m squared minus 3 mn plus 5 n squared close parentheses.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_003c_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"In step 3, use the reverse Distributive Property to factor the expression as 4m open parentheses 2 m squared minus 3 mn plus 5 n squared close parentheses.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167834464468\" data-alt=\"Step 4 is to check by multiplying the factors. By multiplying the factors, we get the original polynomial.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_003d_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 4 is to check by multiplying the factors. By multiplying the factors, we get the original polynomial.\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167826996813\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835238831\">\n<div data-type=\"problem\" id=\"fs-id1167832051959\">\n<p>Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b40ccd2ef6a471f7b2331c43990e932c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#49;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"162\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835332262\">\n<p id=\"fs-id1167835368386\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6a25a496243908000580bad06246a8cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#43;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"150\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167834505596\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167834587406\">\n<div data-type=\"problem\" id=\"fs-id1167835483550\">\n<p id=\"fs-id1167835360244\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c9631bf717a7a4562fab0a487e010cdb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#45;&#54;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#113;&#43;&#57;&#112;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167834505889\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2547cb65a48a0bbe9971f1cf2cbcb98b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#112;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#112;&#113;&#43;&#51;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"146\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167832041602\" class=\"howto\">\n<div data-type=\"title\">Factor the greatest common factor from a polynomial.<\/div>\n<ol id=\"fs-id1167831116496\" type=\"1\" class=\"stepwise\">\n<li>Find the GCF of all the terms of the polynomial.<\/li>\n<li>Rewrite each term as a product using the GCF.<\/li>\n<li>Use the \u201creverse\u201d Distributive Property to factor the expression.<\/li>\n<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167826967230\">\n<div data-type=\"title\">Factor as a Noun and a Verb<\/div>\n<p id=\"fs-id1167835264941\">We use \u201cfactor\u201d as both a noun and a verb:<\/p>\n<div data-type=\"equation\" id=\"fs-id1167835335577\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-17f847baf97505c734d9c7369c5cfe3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#111;&#117;&#110;&#58;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#56;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#32;&#105;&#115;&#32;&#97;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#97;&#99;&#116;&#111;&#114;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#32;&#49;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#86;&#101;&#114;&#98;&#58;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#56;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#97;&#99;&#116;&#111;&#114;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#32;&#102;&#114;&#111;&#109;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#97;&#43;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"389\" style=\"vertical-align: -13px;\" \/><\/div>\n<\/div>\n<div data-type=\"example\" id=\"fs-id1167832226526\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167835323694\">\n<div data-type=\"problem\" id=\"fs-id1167835340040\">\n<p id=\"fs-id1167835379260\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a9b420b7f8bdcd43f83bbe8f7b9712e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#50;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"88\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834448943\">\n<table id=\"fs-id1167835355061\" class=\"unnumbered unstyled\" summary=\"First find the GCF of 5 x cubed and 25 x squared. By factoring, bringing down the common factors and multiplying them, we get the GCF as 5 x squared. We rewrite the polynomial as 5 x squared times x minus 5 x squared times 5. Next we factor the GCF and rewrite as 5 x squared open parentheses x minus 5 close parentheses. Finally we check by multiplying the factors to get the original polynomial.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td colspan=\"2\" data-valign=\"middle\" data-align=\"left\">Find the GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0ad8655a65bb986a62c563c119edd22c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7155232b4163d6aa268d692ce8eebb17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-valign=\"middle\" data-align=\"left\"><span data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_005b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835514387\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_005c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835308604\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_005d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Rewrite each term.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835258142\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_005e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Factor the GCF.<\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_005f_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Check:<\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-75911db447a506057ec558c3bac15eed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&middot;&#120;&#45;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&middot;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#50;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"93\" style=\"vertical-align: -22px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835335871\" class=\"try\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167834505216\">\n<p>Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5b02872275b63007303d667dba57ff31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834432207\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f116c86a7d534d4aa02e15978ff7a852_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835347937\" class=\"try\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167832015530\">\n<p>Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-37eb4ac87ff41ed0ea7b9d0fd178d38b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167834190741\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8aeab34fd2a80efaf7500d1ca3b2d964_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#121;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"example\" id=\"fs-id1167835370672\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167834193968\">\n<p id=\"fs-id1167835301394\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-64fd0f9d7bf3330ab8bd68f9a799fc56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;&#45;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#120;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"181\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831825042\">\n<table id=\"fs-id1167835367729\" class=\"unnumbered unstyled\" summary=\"The GCF of 8 x cubed y minus 10 x squared y squared plus 12 x y cubed is 2xy. Rewriting each term using the GCF, we get 2xy times 4x squared minus 2xy times 5xy plus 2xy times 6 y squared. Factoring out the GCF, we get 2xy open parentheses 4 x squared minus 5xy plus 6 y squared. Finally, we check by multiplying the factors to get the original polynomial.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">The GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8f62f5f2be4c486c30255adc5e536452_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;&#44;&#45;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#44;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#50;&#120;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"198\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p>is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-432dceb60d5e6cd4201c31fe9e547685_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#121;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"32\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835239981\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_007b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"left\"><span data-type=\"media\" id=\"fs-id1167835356022\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_007c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"center\">\u2003\u2003\u2003\u2003\u2003<span data-type=\"media\" id=\"fs-id1167835229282\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_007a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Rewrite each term using the GCF, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-432dceb60d5e6cd4201c31fe9e547685_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#121;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"32\" style=\"vertical-align: -4px;\" \/>\u2003\u2003\u2003\u2003<\/td>\n<td data-valign=\"top\" data-align=\"center\">\u2003\u2003<span data-type=\"media\" id=\"fs-id1167835421099\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_007d_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Factor the GCF.<\/td>\n<td data-valign=\"top\" data-align=\"center\">\u2003\u2003\u2003\u2003\u2003<span data-type=\"media\" id=\"fs-id1167830703991\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_007e_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Check:<\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9d5e5eb697d4db991c9630e9f13df4e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#120;&#121;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#120;&#121;&#43;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#50;&#120;&#121;&middot;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#120;&#121;&middot;&#53;&#120;&#121;&#43;&#50;&#120;&#121;&middot;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;&#45;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#120;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"209\" style=\"vertical-align: -26px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835423184\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835306718\">\n<div data-type=\"problem\" id=\"fs-id1167835310717\">\n<p id=\"fs-id1167832058345\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a455c4f467c4cda60cfeb6c90edfe1c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#120;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"171\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835362706\">\n<p id=\"fs-id1167834131221\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2e3a14330f6fd70d317a3c0f78e37677_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#121;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#121;&#43;&#50;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"161\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167826996512\" class=\"try\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167832152708\">\n<p id=\"fs-id1167831895303\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a5f638c666f25c4a5dadd4fa0440de36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#98;&#43;&#50;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#97;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"156\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834196723\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9c46fb956774f441236ee3117c6661c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#97;&#98;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#97;&#98;&#45;&#51;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"153\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167835327183\">When the leading coefficient is negative, we factor the negative out as part of the GCF.<\/p>\n<div data-type=\"example\" id=\"fs-id1167835346406\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167835262496\">\n<p id=\"fs-id1167832005973\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9b36f83a635d52bf27497905aedb2dd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#43;&#51;&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#97;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"139\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834556901\">\n<p id=\"fs-id1167835330823\">The leading coefficient is negative, so the GCF will be negative.<\/p>\n<table class=\"unnumbered unstyled\" summary=\"We rewrite each term in the polynomial using the GCF minus 4a. So, we get minus 4a times a squared minus open parentheses minus 4 a close parentheses times 9 a plus open parentheses minus 4 a close parentheses times 2. Factoring the GCF, we get minus 4 a open parentheses a squared minus 9a plus 2 close parentheses. Finally, we check by multiplying the factors to get the original polynomial.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"center\"><span data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_008a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Rewrite each term using the GCF, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6fbfcf19b538cd8f06373eeb1677bf1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#97;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"35\" style=\"vertical-align: -1px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"center\"><span data-type=\"media\" id=\"fs-id1167835307398\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_008b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Factor the GCF.<\/td>\n<td data-valign=\"top\" data-align=\"center\"><span data-type=\"media\" id=\"fs-id1167832060518\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_008c_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Check:<\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9a50f4bd79a935b161930de0f25082d4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#52;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#97;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#52;&#97;&middot;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&middot;&#57;&#97;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&middot;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#52;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#43;&#51;&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#97;&#10003;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"61\" width=\"215\" style=\"vertical-align: -24px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835237838\" class=\"try\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167831825025\">\n<p id=\"fs-id1167831846710\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0572bf197457637574955204e3a2459f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#43;&#49;&#54;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#98;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"134\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167832153158\">\n<p id=\"fs-id1167834395016\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c2c5dcb6c143c9e2179f423ea8a62848_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#98;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#98;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"130\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167834423260\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835308305\">\n<div data-type=\"problem\" id=\"fs-id1167835329145\">\n<p id=\"fs-id1167835366743\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-479e1be5edf7103d99c0edce8a60253f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#43;&#50;&#49;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#52;&#97;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"148\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835341033\">\n<p id=\"fs-id1167835324798\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a9f2fda8f7b51aa8af7ac8ad81ab7fd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#97;&#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=\"136\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1167834252720\">So far our greatest common factors have been monomials. In the next example, the greatest common factor is a binomial.<\/p>\n<div data-type=\"example\" id=\"fs-id1167834308954\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167832055694\">\n<p>Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-030e410a65fe31badd63ca09dae3c266_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#121;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"169\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834061707\">\n<p id=\"fs-id1167835338725\">The GCF is the binomial <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-531d11c8cb070b8771783c5f2d3a4ece_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#55;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"44\" style=\"vertical-align: -4px;\" \/><\/p>\n<table class=\"unnumbered unstyled\" summary=\"The polynomial is 3y open parentheses y plus 7 close parentheses minus 4 open parentheses y plus 7 close parentheses. Factor the GCF open parentheses y plus 7 close parentheses. We get open parentheses y plus 7 close parentheses open parentheses 3y minus 4 close parentheses. Check on your own by multiplying.\" data-label=\"\">\n<tbody>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<td data-valign=\"top\" data-align=\"center\"><span data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_009a_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Factor the GCF, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-abb6c3db64ad04ca41318ebad10269ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"60\" style=\"vertical-align: -4px;\" \/><\/td>\n<td data-valign=\"top\" data-align=\"center\"><span data-type=\"media\" id=\"fs-id1167828410744\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_009b_img.jpg\" data-media-type=\"image\/jpeg\" alt=\".\" \/><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-valign=\"top\" data-align=\"left\">Check on your own by multiplying.\u2003\u2003\u2003<\/td>\n<td data-valign=\"top\" data-align=\"left\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835329782\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167834472269\">\n<div data-type=\"problem\" id=\"fs-id1167835349236\">\n<p>Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-eeba9204a44f222df2720393f9f8ea4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"188\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835307821\">\n<p id=\"fs-id1167826994245\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cc03cfbff16f26f03f2dfb8dee041ad2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#109;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"130\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"try\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167831116851\">\n<p id=\"fs-id1167834133021\">Factor: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2507729a363618ab41c414540746e33a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#110;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"173\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834537857\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ebb762b5f8b779a4a694259028f5f5b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#110;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"120\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id1167834438900\">\n<h3 data-type=\"title\">Factor by Grouping<\/h3>\n<p id=\"fs-id1167835340140\">Sometimes there is no common factor of all the terms of a polynomial. When there are four terms we separate the polynomial into two parts with two terms in each part. Then look for the <span data-type=\"term\" class=\"no-emphasis\">GCF<\/span> in each part. If the polynomial can be factored, you will find a common factor emerges from both parts. Not all polynomials can be factored. Just like some numbers are <span data-type=\"term\" class=\"no-emphasis\">prime<\/span>, some polynomials are prime.<\/p>\n<div data-type=\"example\" class=\"textbox textbox--examples\">\n<div data-type=\"title\">How to Factor a Polynomial by Grouping<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835594921\">\n<div data-type=\"problem\" id=\"fs-id1167832041513\">\n<p>Factor by grouping: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7fb4d2381ffce996976e59506e227e3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#121;&#43;&#51;&#121;&#43;&#50;&#120;&#43;&#54;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"135\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\"><span data-type=\"media\" data-alt=\"Step 1 is to group the terms with common factors. There is no greatest common factor in all the four terms of xy plus 3y plus 2x plus 6. So, separate the first two terms from the second two.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_010a_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 1 is to group the terms with common factors. There is no greatest common factor in all the four terms of xy plus 3y plus 2x plus 6. So, separate the first two terms from the second two.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167835345071\" data-alt=\"Step 2 is to factor out the common factor in each group. By factoring the GCF from the first 2 terms, we get y open parentheses x plus 3 close parentheses plus 2x plus 6. Factoring the GCF from the second 2 terms, we get y open parentheses x plus 3 close parentheses plus 2 open parentheses x plus 3 close parentheses.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_010b_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 2 is to factor out the common factor in each group. By factoring the GCF from the first 2 terms, we get y open parentheses x plus 3 close parentheses plus 2x plus 6. Factoring the GCF from the second 2 terms, we get y open parentheses x plus 3 close parentheses plus 2 open parentheses x plus 3 close parentheses.\" \/><\/span><span data-type=\"media\" id=\"fs-id1167835190796\" data-alt=\"Step 3 is to factor the common factor from the expression. Notice that each term has a common factor of x plus 3. By factoring this out, we get open parentheses x plus 3 close parentheses open parentheses y plus 2 close parentheses\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_010c_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 3 is to factor the common factor from the expression. Notice that each term has a common factor of x plus 3. By factoring this out, we get open parentheses x plus 3 close parentheses open parentheses y plus 2 close parentheses\" \/><\/span><span data-type=\"media\" data-alt=\"Step 4 is to check by multiplying the expressions to get the result xy plus 3y plus 2x plus 6.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_010d_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"Step 4 is to check by multiplying the expressions to get the result xy plus 3y plus 2x plus 6.\" \/><\/span><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835305027\">\n<div data-type=\"problem\">\n<p>Factor by grouping: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4bf473673feb0191e2b5b70a1efb6216_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#121;&#43;&#56;&#121;&#43;&#51;&#120;&#43;&#50;&#52;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835339253\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-787810279666495a476a694333e97e39_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167832060644\" class=\"try\">\n<div data-type=\"exercise\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167834515926\">Factor by grouping: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-cdc27c72beb03f9eef52f0aa84f59f36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#98;&#43;&#55;&#98;&#43;&#56;&#97;&#43;&#53;&#54;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"139\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835464002\">\n<p id=\"fs-id1167835188009\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5bb6142f3f65f4b6ce80ab546a888b79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"107\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835187158\" class=\"howto\">\n<div data-type=\"title\">Factor by grouping.<\/div>\n<ol id=\"fs-id1167835308131\" type=\"1\" class=\"stepwise\">\n<li>Group terms with common factors.<\/li>\n<li>Factor out the common factor in each group.<\/li>\n<li>Factor the common factor from the expression.<\/li>\n<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/div>\n<div data-type=\"example\" id=\"fs-id1167835321886\" class=\"textbox textbox--examples\">\n<div data-type=\"exercise\" id=\"fs-id1167831919943\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167832195761\">Factor by grouping: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4dd71a81fca0b0f73f0a45c736d4428e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#45;&#50;&#120;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"130\" style=\"vertical-align: -2px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-08944852c90b1014bb62ae13a41ff15f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#45;&#52;&#120;&#43;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"143\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167835325203\"><span class=\"token\">\u24d0<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-080811dc99b8a2c604c6206b3d21ca1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#114;&#101;&#32;&#105;&#115;&#32;&#110;&#111;&#32;&#71;&#67;&#70;&#32;&#105;&#110;&#32;&#97;&#108;&#108;&#32;&#102;&#111;&#117;&#114;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#45;&#50;&#120;&#45;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#101;&#112;&#97;&#114;&#97;&#116;&#101;&#32;&#105;&#110;&#116;&#111;&#32;&#116;&#119;&#111;&#32;&#112;&#97;&#114;&#116;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#50;&#120;&#45;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#97;&#99;&#116;&#111;&#114;&#32;&#116;&#104;&#101;&#32;&#71;&#67;&#70;&#32;&#102;&#114;&#111;&#109;&#32;&#98;&#111;&#116;&#104;&#32;&#112;&#97;&#114;&#116;&#115;&#46;&#32;&#66;&#101;&#32;&#99;&#97;&#114;&#101;&#102;&#117;&#108;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#105;&#116;&#104;&#32;&#116;&#104;&#101;&#32;&#115;&#105;&#103;&#110;&#115;&#32;&#119;&#104;&#101;&#110;&#32;&#102;&#97;&#99;&#116;&#111;&#114;&#105;&#110;&#103;&#32;&#116;&#104;&#101;&#32;&#71;&#67;&#70;&#32;&#102;&#114;&#111;&#109;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#104;&#101;&#32;&#108;&#97;&#115;&#116;&#32;&#116;&#119;&#111;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#97;&#99;&#116;&#111;&#114;&#32;&#111;&#117;&#116;&#32;&#116;&#104;&#101;&#32;&#99;&#111;&#109;&#109;&#111;&#110;&#32;&#102;&#97;&#99;&#116;&#111;&#114;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#104;&#101;&#99;&#107;&#32;&#111;&#110;&#32;&#121;&#111;&#117;&#114;&#32;&#111;&#119;&#110;&#32;&#98;&#121;&#32;&#109;&#117;&#108;&#116;&#105;&#112;&#108;&#121;&#105;&#110;&#103;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"151\" width=\"600\" style=\"vertical-align: -69px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><\/p>\n<div data-type=\"newline\"><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-66420e2e35417b2af94cceb64d35a473_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#101;&#114;&#101;&#32;&#105;&#115;&#32;&#110;&#111;&#32;&#71;&#67;&#70;&#32;&#105;&#110;&#32;&#97;&#108;&#108;&#32;&#102;&#111;&#117;&#114;&#32;&#116;&#101;&#114;&#109;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#45;&#52;&#120;&#43;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#101;&#112;&#97;&#114;&#97;&#116;&#101;&#32;&#105;&#110;&#116;&#111;&#32;&#116;&#119;&#111;&#32;&#112;&#97;&#114;&#116;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#52;&#120;&#43;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#97;&#99;&#116;&#111;&#114;&#32;&#116;&#104;&#101;&#32;&#71;&#67;&#70;&#32;&#102;&#114;&#111;&#109;&#32;&#98;&#111;&#116;&#104;&#32;&#112;&#97;&#114;&#116;&#115;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#97;&#99;&#116;&#111;&#114;&#32;&#111;&#117;&#116;&#32;&#116;&#104;&#101;&#32;&#99;&#111;&#109;&#109;&#111;&#110;&#32;&#102;&#97;&#99;&#116;&#111;&#114;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#104;&#101;&#99;&#107;&#32;&#111;&#110;&#32;&#121;&#111;&#117;&#114;&#32;&#111;&#119;&#110;&#32;&#98;&#121;&#32;&#109;&#117;&#108;&#116;&#105;&#112;&#108;&#121;&#105;&#110;&#103;&#46;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"106\" width=\"589\" style=\"vertical-align: -47px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" id=\"fs-id1167835268015\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167835299941\">\n<div data-type=\"problem\" id=\"fs-id1167835585149\">\n<p>Factor by grouping: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5a36387e88bca237ae2078846ca3849a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#120;&#45;&#53;&#120;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"139\" style=\"vertical-align: -2px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-05fee7b955b53cacc42dd2880b53a86d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#54;&#120;&#45;&#49;&#53;&#120;&#43;&#49;&#50;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"178\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834183816\">\n<p id=\"fs-id1167835595339\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-34a31a4033d905a5781ed903f19b5b54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c60c5a090f806a7e16e0c8e96f82cefd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#120;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"128\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\" class=\"try\">\n<div data-type=\"exercise\" id=\"fs-id1167826814135\">\n<div data-type=\"problem\" id=\"fs-id1167834430060\">\n<p id=\"fs-id1167826803903\">Factor by grouping: <span class=\"token\">\u24d0<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0a6b6bec08aa5bcea0aa800a250fe648_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#121;&#45;&#55;&#121;&#45;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -4px;\" \/> <span class=\"token\">\u24d1<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e4923bf4d86d576b6c125bbb52e161dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#56;&#109;&#45;&#51;&#53;&#109;&#43;&#49;&#53;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"195\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167828410732\">\n<p id=\"fs-id1167835202851\"><span class=\"token\">\u24d0<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4c6135dc1bcd04883aac4fe206b5ddb4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"108\" style=\"vertical-align: -4px;\" \/><\/p>\n<div data-type=\"newline\"><\/div>\n<p><span class=\"token\">\u24d1<\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f1711f8b4a43ebe92f101e06e3d8ffcc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#109;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#109;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"139\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167831923591\">\n<h3 data-type=\"title\">Key Concepts<\/h3>\n<ul id=\"fs-id1167834433471\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">How to find the greatest common factor (GCF) of two expressions.<\/strong>\n<ol id=\"fs-id1167827987881\" type=\"1\" class=\"stepwise\">\n<li>Factor each coefficient into primes. Write all variables with exponents in expanded form.<\/li>\n<li>List all factors\u2014matching common factors in a column. In each column, circle the common factors.<\/li>\n<li>Bring down the common factors that all expressions share.<\/li>\n<li>Multiply the factors.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Distributive Property:<\/strong> If <em data-effect=\"italics\">a<\/em>, <em data-effect=\"italics\">b<\/em>, and <em data-effect=\"italics\">c<\/em> are real numbers, then\n<div data-type=\"newline\"><\/div>\n<div data-type=\"equation\" id=\"fs-id1167831835907\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-9dc3219c7fceb55c81eca5b3049cd20b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#97;&#98;&#43;&#97;&#99;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#98;&#43;&#97;&#99;&#61;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"348\" style=\"vertical-align: -4px;\" \/><\/div>\n<div data-type=\"newline\"><\/div>\n<p> The form on the left is used to multiply. The form on the right is used to factor.<\/li>\n<li><strong data-effect=\"bold\">How to factor the greatest common factor from a polynomial.<\/strong>\n<ol id=\"fs-id1167832054265\" type=\"1\" class=\"stepwise\">\n<li>Find the GCF of all the terms of the polynomial.<\/li>\n<li>Rewrite each term as a product using the GCF.<\/li>\n<li>Use the \u201creverse\u201d Distributive Property to factor the expression.<\/li>\n<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Factor as a Noun and a Verb:<\/strong> We use \u201cfactor\u201d as both a noun and a verb.\n<div data-type=\"newline\"><\/div>\n<div data-type=\"equation\" id=\"fs-id1167831116300\" class=\"unnumbered\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7d3052aaeb70812def83bb82fb74011a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#111;&#117;&#110;&#58;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#55;&#32;&#105;&#115;&#32;&#97;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#97;&#99;&#116;&#111;&#114;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#32;&#49;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#86;&#101;&#114;&#98;&#58;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#97;&#99;&#116;&#111;&#114;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#32;&#102;&#114;&#111;&#109;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#97;&#43;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"37\" width=\"247\" style=\"vertical-align: -13px;\" \/><\/div>\n<\/li>\n<li><strong data-effect=\"bold\">How to factor by grouping.<\/strong>\n<ol id=\"fs-id1167826801698\" type=\"1\" class=\"stepwise\">\n<li>Group terms with common factors.<\/li>\n<li>Factor out the common factor in each group.<\/li>\n<li>Factor the common factor from the expression.<\/li>\n<li>Check by multiplying the factors.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox\" data-depth=\"1\" id=\"fs-id1167835215319\">\n<div class=\"practice-perfect\" data-depth=\"2\" id=\"fs-id1167834308203\">\n<h4 data-type=\"title\">Practice Makes Perfect<\/h4>\n<p id=\"fs-id1167835307743\"><strong data-effect=\"bold\">Find the Greatest Common Factor of Two or More Expressions<\/strong><\/p>\n<p id=\"fs-id1167835336534\">In the following exercises, find the greatest common factor.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167831890415\">\n<div data-type=\"problem\" id=\"fs-id1167834556665\">\n<p id=\"fs-id1167834403274\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e2224b35f321d743c142c9e08fd66a18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#113;&#44;&#49;&#50;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835337582\">\n<p id=\"fs-id1167830868646\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d8d1e8e2f094da0cc218fc1de808d7ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#112;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"26\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834065925\">\n<div data-type=\"problem\" id=\"fs-id1167831883509\">\n<p id=\"fs-id1167835333240\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d8abb0a2670da3e0019cba6a1d0b697a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#44;&#49;&#48;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832059919\">\n<div data-type=\"problem\" id=\"fs-id1167832133982\">\n<p id=\"fs-id1167835237682\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-499a2e83cae0d27186b4fdf269cc4fbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#44;&#51;&#48;&#123;&#109;&#125;&#94;&#123;&#53;&#125;&#123;&#110;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"125\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835173235\">\n<p id=\"fs-id1167835235925\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e474101f81c4119eea53625fd801e3ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#123;&#110;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835186941\">\n<div data-type=\"problem\" id=\"fs-id1167834239042\">\n<p id=\"fs-id1167831116606\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d99519b10440c37d8b2d47aa4d560bb0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#44;&#52;&#50;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#123;&#121;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835349597\">\n<div data-type=\"problem\" id=\"fs-id1167835306791\">\n<p id=\"fs-id1167835374776\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f4c1ecf041279c2ab3ea5c40816c372e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#44;&#49;&#50;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#52;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835419990\">\n<p id=\"fs-id1167835418113\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-02baaffe4ddb6a44400eb7ba175e566c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835421936\">\n<div data-type=\"problem\" id=\"fs-id1167834538766\">\n<p id=\"fs-id1167835423323\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-bf20ba1476230af9371f18125364c567_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#44;&#50;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#44;&#52;&#48;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835187200\">\n<div data-type=\"problem\" id=\"fs-id1167831871864\">\n<p id=\"fs-id1167834064707\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c74b3054a02b9e0c18e912bc3e1f94f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#44;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#121;&#44;&#53;&#123;&#120;&#125;&#94;&#123;&#53;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"156\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834156917\">\n<p id=\"fs-id1167832075976\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2923cc39c6d7bc856c1b63f66e065979_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"36\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835380762\">\n<div data-type=\"problem\" id=\"fs-id1167832036187\">\n<p id=\"fs-id1167834357146\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ce7948ec199441acd4ef55ea98ff3997_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#44;&#52;&#53;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#44;&#57;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#123;&#113;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"158\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167835380474\"><strong data-effect=\"bold\">Factor the Greatest Common Factor from a Polynomial<\/strong><\/p>\n<p id=\"fs-id1167834062656\">In the following exercises, factor the greatest common factor from each polynomial.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167835321212\">\n<div data-type=\"problem\" id=\"fs-id1167834097776\">\n<p id=\"fs-id1167831117445\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ebfe857d6de33f9e98b471b0176838ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#109;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"55\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834403394\">\n<p id=\"fs-id1167834246589\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-25dc6a998bfa12795f326b9b7e77e356_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#109;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"80\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167830697830\">\n<div data-type=\"problem\" id=\"fs-id1167835191989\">\n<p id=\"fs-id1167834191594\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d7c26f6ceb770a456b95a0a1aedbc80a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#112;&#43;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"64\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167831883792\">\n<div data-type=\"problem\" id=\"fs-id1167835328863\">\n<p id=\"fs-id1167835229373\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-754b39a85b11f41442c53267d6511936_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#110;&#45;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"59\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167830693436\">\n<p id=\"fs-id1167831883382\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e478a99f4856e944f6d9b432f1d9ccf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835381410\">\n<div data-type=\"problem\" id=\"fs-id1167835230324\">\n<p id=\"fs-id1167834403298\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-dd64d1ac24d4d85e33e2d92d2189ad59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;&#98;&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"65\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834192385\">\n<div data-type=\"problem\" id=\"fs-id1167835421055\">\n<p id=\"fs-id1167835233290\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d37daec7b49c49d44e3ccbf85670901a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#120;&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"98\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835363865\">\n<p id=\"fs-id1167835301588\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-10eac7b8a8b138c0e7d072602c133cf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#120;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"115\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834185484\">\n<div data-type=\"problem\" id=\"fs-id1167835513601\">\n<p id=\"fs-id1167835358548\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-664a2a337a922fc07d53def43034f474_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#56;&#121;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832043698\">\n<div data-type=\"problem\" id=\"fs-id1167834219471\">\n<p id=\"fs-id1167835310143\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3fb8ab118fa6c57bb8651b54ccc4a5b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#112;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"95\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167828447183\">\n<p id=\"fs-id1167826978899\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4f8ccb29118d92ac678ae351e9d2ff09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#112;&#43;&#49;&#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>\n<div data-type=\"exercise\" id=\"fs-id1167828421716\">\n<div data-type=\"problem\" id=\"fs-id1167831040276\">\n<p id=\"fs-id1167835389992\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-682d7dee7eef2acb05dc225900b7d61e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#52;&#113;&#43;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832042721\">\n<div data-type=\"problem\" id=\"fs-id1167834462857\">\n<p id=\"fs-id1167826993902\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2fc87bb5a60031b988b2e31f1fd60de7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#43;&#49;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831883492\">\n<p id=\"fs-id1167831922684\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c26c3e186a9b8a7920dfcae93bc32aed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835629180\">\n<div data-type=\"problem\" id=\"fs-id1167834464406\">\n<p id=\"fs-id1167832151513\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-72e96a2d5a9f782b0e9bb64c649df850_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"84\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835483676\">\n<div data-type=\"problem\" id=\"fs-id1167834280064\">\n<p id=\"fs-id1167834194415\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-38489720e01153e829082926006d7ec6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#48;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"134\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835351982\">\n<p id=\"fs-id1167831890778\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f3c485d163455c737d76c631684bd78a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"125\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167831880194\">\n<div data-type=\"problem\" id=\"fs-id1167832041560\">\n<p id=\"fs-id1167834555206\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-efa01d1e1d08c12e89758796547e35cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#48;&#109;&#43;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"127\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832053525\">\n<div data-type=\"problem\" id=\"fs-id1167835233897\">\n<p id=\"fs-id1167830963422\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b05f1cbe3f8ad122e2793fdc08fa3fe3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#53;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"142\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167826808708\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7f37975afc56b042c7f2a65b848d47f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"134\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835233120\">\n<div data-type=\"problem\" id=\"fs-id1167835231120\">\n<p id=\"fs-id1167835301823\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3c0a7f8f6ef327cadf31bd6b6c440cb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#48;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"140\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835514026\">\n<div data-type=\"problem\" id=\"fs-id1167835513221\">\n<p id=\"fs-id1167834556053\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-2372f97c3c20427befc26c33c33fdc24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#48;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"174\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831920308\">\n<p id=\"fs-id1167832051769\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-5aaeebf77da166451d623c11c5e3fa9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#43;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"150\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834505039\">\n<div data-type=\"problem\" id=\"fs-id1167834396469\">\n<p id=\"fs-id1167834506190\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6ddafecf3466c9e382ed31d987687746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#53;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#56;&#123;&#113;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"170\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835327156\">\n<div data-type=\"problem\" id=\"fs-id1167835362634\">\n<p id=\"fs-id1167834053526\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-3bcce84b573538c41a1e6dd414df3352_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;&#45;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#120;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"176\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834463054\">\n<p id=\"fs-id1167834463056\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-191067058939a9a318e559261846f58e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#121;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#121;&#43;&#51;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"161\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834395336\">\n<div data-type=\"problem\" id=\"fs-id1167834395338\">\n<p id=\"fs-id1167831910118\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-08fc2cb2f69a1295b2618fead06253a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#98;&#43;&#54;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#56;&#97;&#123;&#98;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"169\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826995349\">\n<div data-type=\"problem\" id=\"fs-id1167835236135\">\n<p id=\"fs-id1167835236137\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-18d5a3608b5d8e24bad24023e3d124d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: -1px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835303487\">\n<p id=\"fs-id1167835303489\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8891c01a67d1fc2d613481a3843b9c54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834289446\">\n<div data-type=\"problem\" id=\"fs-id1167835387157\">\n<p id=\"fs-id1167835387159\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b90c960e0ada8a6825284fdacdfdde19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#98;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"68\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835416377\">\n<div data-type=\"problem\" id=\"fs-id1167832226484\">\n<p id=\"fs-id1167832226486\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8bc9c263e08f6a667ec7fbab1dead4ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#49;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"137\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834300326\">\n<p id=\"fs-id1167831847191\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-35205cee22662311f409bd6955576cfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"138\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832058680\">\n<div data-type=\"problem\" id=\"fs-id1167834185856\">\n<p id=\"fs-id1167834079542\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c75dbcb208d30b0b7d796d6da254965f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#43;&#51;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"144\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835417781\">\n<div data-type=\"problem\" id=\"fs-id1167835417783\">\n<p id=\"fs-id1167834300625\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8eeeb1d05c900acad0a4426c58ab7a65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#113;&#45;&#49;&#50;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#54;&#112;&#123;&#113;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"183\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835422237\">\n<p id=\"fs-id1167834060402\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-624f35dff3017fed042f7d7fa76f7842_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#112;&#113;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#112;&#113;&#45;&#52;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"160\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835310781\">\n<div data-type=\"problem\" id=\"fs-id1167835311413\">\n<p id=\"fs-id1167835311415\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-de78c28976e3951129404c2d1b1b1e61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#98;&#45;&#49;&#50;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#56;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"182\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835337185\">\n<div data-type=\"problem\" id=\"fs-id1167835213524\">\n<p id=\"fs-id1167834229188\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-912ad698e4a6f749ed76db5820d979c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"164\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831890913\">\n<p id=\"fs-id1167826814057\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e4d80d20184793c185b79356551ccc0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"119\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834120568\">\n<div data-type=\"problem\" id=\"fs-id1167834120570\">\n<p id=\"fs-id1167827988062\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-4aa702d284432cdaef981c8ab2937f13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"167\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835381458\">\n<div data-type=\"problem\" id=\"fs-id1167835381460\">\n<p id=\"fs-id1167835319923\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e943f389eb4d1ec83b695c1aa673ee48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#98;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"165\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834429474\">\n<p id=\"fs-id1167835410518\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-8317f1be24973878632079adac21daa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#98;&#45;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"123\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167827967167\">\n<div data-type=\"problem\" id=\"fs-id1167827967169\">\n<p id=\"fs-id1167835503992\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-d8690439c21e9459d0cd0370bafd3df8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"180\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167835367819\"><strong data-effect=\"bold\">Factor by Grouping<\/strong><\/p>\n<p id=\"fs-id1167826966819\">In the following exercises, factor by grouping.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167826966822\">\n<div data-type=\"problem\" id=\"fs-id1167835353655\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c41f28810842617affead5d38b23ee75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#98;&#43;&#53;&#97;&#43;&#51;&#98;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"134\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167830964376\">\n<p id=\"fs-id1167830964378\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-a042a63ced1b53e5002eed5918520460_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"107\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834583319\">\n<div data-type=\"problem\" id=\"fs-id1167834583321\">\n<p id=\"fs-id1167834562482\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ae45661cbb925cc0d2ec325866285baf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#100;&#43;&#54;&#99;&#43;&#52;&#100;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"135\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167831824322\">\n<div data-type=\"problem\" id=\"fs-id1167831824324\">\n<p id=\"fs-id1167835306581\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-429b465d1514f1908edbe295bd8acf5e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#121;&#43;&#52;&#48;&#121;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"135\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167827988156\">\n<p id=\"fs-id1167835355764\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-da1affbae25387fb35ad90b297bac35b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#121;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"117\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835609625\">\n<div data-type=\"problem\" id=\"fs-id1167835609627\">\n<p id=\"fs-id1167826857108\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-12815ff2a948eefb3a6e503bbbb474d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#121;&#43;&#50;&#52;&#121;&#43;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"154\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\">\n<div data-type=\"problem\" id=\"fs-id1167830704254\">\n<p id=\"fs-id1167830704256\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f68f08093e98f9086280ff4a0d94ffb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#118;&#45;&#57;&#117;&#43;&#50;&#118;&#45;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"139\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835365743\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7f934eecebf8aae99d1fa0d7a022814c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#118;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"109\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835288046\">\n<div data-type=\"problem\" id=\"fs-id1167835288049\">\n<p id=\"fs-id1167834430816\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ff0cd233d3353d014245e9844c5c8d6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#113;&#45;&#49;&#48;&#112;&#43;&#56;&#113;&#45;&#56;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"146\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167830702860\">\n<div data-type=\"problem\" id=\"fs-id1167830702862\">\n<p id=\"fs-id1167830960717\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-345d0835b90db3811909b68e376a524f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#45;&#117;&#43;&#54;&#117;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"121\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835483711\">\n<p id=\"fs-id1167835483713\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0d3e71d1e3d014d17e9ed7b3b34e8f9d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#43;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"110\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167827957103\">\n<div data-type=\"problem\" id=\"fs-id1167827957105\">\n<p id=\"fs-id1167831106969\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0da39ed27c8a69877a4157a75bfe22df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#43;&#52;&#120;&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"121\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835420263\">\n<div data-type=\"problem\" id=\"fs-id1167835420266\">\n<p id=\"fs-id1167834473406\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-22d0073ef11d81a98c335b8748f4fdd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#112;&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834556761\">\n<p id=\"fs-id1167834472577\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-506c7975b23f7b145c181320b47dd302_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#112;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#112;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"125\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835279990\">\n<div data-type=\"problem\" id=\"fs-id1167834463003\">\n<p id=\"fs-id1167834463006\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-db540e7446724a934383e5627cac9e40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#45;&#56;&#113;&#45;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826801811\">\n<div data-type=\"problem\" id=\"fs-id1167826801814\">\n<p id=\"fs-id1167826997425\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-97ca321f6420af1b19d8263342c2e5e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#110;&#45;&#54;&#109;&#45;&#52;&#110;&#43;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"153\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167831881876\">\n<p id=\"fs-id1167831959287\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-50b08fadbb44456bcb6f61b80799b9fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167832067463\">\n<div data-type=\"problem\" id=\"fs-id1167830838248\">\n<p id=\"fs-id1167830838250\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-e44f75a4b357dcfda0ca0a9c3dfb4e19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#114;&#45;&#114;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"116\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835307679\">\n<div data-type=\"problem\" id=\"fs-id1167835305778\">\n<p id=\"fs-id1167835305780\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-adae153129eb11e82be08745f1b3cca0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#52;&#120;&#45;&#53;&#120;&#43;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"156\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835370068\">\n<p id=\"fs-id1167834094604\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-6bb883f6844ce52de70cbc3825a721bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#120;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"119\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835309245\">\n<div data-type=\"problem\" id=\"fs-id1167835309247\">\n<p id=\"fs-id1167834464434\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-0ed9cc81174249a92918aa7c3a458552_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#54;&#120;&#45;&#51;&#120;&#43;&#50;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"157\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1167834120191\"><strong data-effect=\"bold\">Mixed Practice<\/strong><\/p>\n<p id=\"fs-id1167835319069\">In the following exercises, factor.<\/p>\n<div data-type=\"exercise\" id=\"fs-id1167834516217\">\n<div data-type=\"problem\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c87b31bbc28dd09ec2fd4061ef6c69f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835360501\">\n<p id=\"fs-id1167832058205\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-20a98beda4e6a8c1b1e1869118fece98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#120;&#121;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#43;&#50;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"116\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835352834\">\n<div data-type=\"problem\" id=\"fs-id1167835352836\">\n<p id=\"fs-id1167834228318\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-ff87f8a304a402f7e4600a8ae8e42a68_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#45;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#43;&#49;&#50;&#120;&#123;&#121;&#125;&#94;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"179\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167826802847\">\n<div data-type=\"problem\" id=\"fs-id1167835330068\">\n<p id=\"fs-id1167835330070\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-35bb8f42ba167dfcb8f85e920d3411f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#120;&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"155\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167834501736\">\n<p id=\"fs-id1167834501738\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f7a0520e3748fd3ccf7900c553224f56_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;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"128\" style=\"vertical-align: -7px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\">\n<div data-type=\"problem\">\n<p id=\"fs-id1167831881339\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-10b2afa2e15afa7ce8bf446e0883f1bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#120;&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"119\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835365610\">\n<div data-type=\"problem\" id=\"fs-id1167835363965\">\n<p id=\"fs-id1167835363967\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-7b3e85e578b5c0d68a557b3f0b7577b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#120;&#121;&#43;&#53;&#120;&#43;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167835311280\">\n<p id=\"fs-id1167835358348\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-b20510bf55410adad55d86d2e634bcaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"111\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167835304678\">\n<div data-type=\"problem\" id=\"fs-id1167835304680\">\n<p id=\"fs-id1167835304683\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-45fdf9eb1e52827f308c3589dc7454c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"146\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"writing\" data-depth=\"2\" id=\"fs-id1167834095298\">\n<h4 data-type=\"title\">Writing Exercises<\/h4>\n<div data-type=\"exercise\" id=\"fs-id1167834535535\">\n<div data-type=\"problem\" id=\"fs-id1167835239421\">\n<p id=\"fs-id1167835239423\">What does it mean to say a polynomial is in factored form?<\/p>\n<\/div>\n<div data-type=\"solution\">\n<p id=\"fs-id1167835368947\">Answers will vary.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167828420166\">\n<div data-type=\"problem\" id=\"fs-id1167835585152\">\n<p id=\"fs-id1167835585154\">How do you check result after factoring a polynomial?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167831985770\">\n<div data-type=\"problem\" id=\"fs-id1167831911253\">\n<p id=\"fs-id1167831911255\">The greatest common factor of 36 and 60 is 12. Explain what this means.<\/p>\n<\/div>\n<div data-type=\"solution\" id=\"fs-id1167828420268\">\n<p id=\"fs-id1167828420270\">Answers will vary.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" id=\"fs-id1167834131452\">\n<div data-type=\"problem\" id=\"fs-id1167832138624\">\n<p id=\"fs-id1167832138626\">What is the GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-314e61e04d25b2e8b7eab3fd115f6d63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#44;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"46\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-89179e049f1bd9ab072e081ebfb71558_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#49;&#48;&#125;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"32\" style=\"vertical-align: -4px;\" \/> Write a general rule that tells you how to find the GCF of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-f27bfab9ea5eebfe12389e93faedeee4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#97;&#125;&#44;&#123;&#121;&#125;&#94;&#123;&#98;&#125;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"45\" style=\"vertical-align: -4px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/ql-cache\/quicklatex.com-c31f0ea2065af989549d6437b93ed669_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#99;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"20\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"2\" id=\"fs-id1167834552513\">\n<h4 data-type=\"title\">Self Check<\/h4>\n<p><span class=\"token\">\u24d0<\/span> After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.<\/p>\n<p><span data-type=\"media\" id=\"fs-id1167835514036\" data-alt=\"This table has 4 columns, 3 rows and a header row. The header row labels each column I can, confidently, with some help and no I don\u2019t get it. The first column has the following statements: find the greatest common factor of 2 or more expressions, factor the greatest common factor from a polynomial, factor by grouping. The remaining columns are blank.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-content\/uploads\/sites\/599\/2018\/12\/CNX_IntAlg_Figure_06_01_201_img_new.jpg\" data-media-type=\"image\/jpeg\" alt=\"This table has 4 columns, 3 rows and a header row. The header row labels each column I can, confidently, with some help and no I don\u2019t get it. The first column has the following statements: find the greatest common factor of 2 or more expressions, factor the greatest common factor from a polynomial, factor by grouping. The remaining columns are blank.\" \/><\/span><\/p>\n<p id=\"fs-id1167831835712\"><span class=\"token\">\u24d1<\/span> If most of your checks were:<\/p>\n<p id=\"fs-id1167830960474\"><strong data-effect=\"bold\">\u2026confidently.<\/strong> Congratulations! You have achieved your goals in this section! Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific!<\/p>\n<p id=\"fs-id1167835360981\"><strong data-effect=\"bold\">\u2026with some help.<\/strong> This must be addressed quickly as topics you do not master become potholes in your road to success. Math is sequential &#8211; every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?<\/p>\n<p id=\"fs-id1167835352370\"><strong data-effect=\"bold\">\u2026no &#8211; I don\u2019t get it!<\/strong> This is critical and you must not ignore it. You need to get help immediately or you will quickly be overwhelmed. See your instructor as soon as possible to discuss your situation. Together you can come up with a plan to get you the help you need.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h3 data-type=\"glossary-title\">Glossary<\/h3>\n<dl id=\"fs-id1167835371075\">\n<dt>factoring<\/dt>\n<dd id=\"fs-id1167835371080\">Splitting a product into factors is called factoring.<\/dd>\n<\/dl>\n<dl id=\"fs-id1167834535267\">\n<dt>greatest common factor<\/dt>\n<dd id=\"fs-id1167834346320\">The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of all the expressions.<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":103,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2992","chapter","type-chapter","status-publish","hentry"],"part":2962,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/2992","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/users\/103"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/2992\/revisions"}],"predecessor-version":[{"id":15252,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/2992\/revisions\/15252"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/parts\/2962"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapters\/2992\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/media?parent=2992"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/pressbooks\/v2\/chapter-type?post=2992"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/contributor?post=2992"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/algebraintermediate\/wp-json\/wp\/v2\/license?post=2992"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}