{"id":1898,"date":"2021-05-19T16:45:50","date_gmt":"2021-05-19T16:45:50","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/divide-polynomials\/"},"modified":"2021-06-22T22:43:16","modified_gmt":"2021-06-22T22:43:16","slug":"divide-polynomials","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/math53\/chapter\/divide-polynomials\/","title":{"raw":"6.6 Divide Polynomials","rendered":"6.6 Divide Polynomials"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Divide a polynomial by a monomial<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Divide a Polynomial by a Monomial<\/h1>\n<p id=\"fs-id1169597495901\">In the last chapter, you learned how to divide a monomial by a monomial. As you continue to build up your knowledge of polynomials the next procedure is to divide a polynomial of two or more terms by a <span class=\"no-emphasis\" data-type=\"term\">monomial<\/span>.<\/p>\n<p id=\"fs-id1169597414468\">The method we\u2019ll use to divide a polynomial by a monomial is based on the properties of fraction addition. So we\u2019ll start with an example to review fraction addition.<\/p>\n\n<table id=\"eip-903\" summary=\".\">\n<tbody>\n<tr>\n<td>The sum,<\/td>\n<td>\\(\\dfrac{y}{5}+\\dfrac{2}{5}\\),<\/td>\n<\/tr>\n<tr>\n<td>simplifies to<\/td>\n<td>\\(\\dfrac{y+2}{5}\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597690628\">Now we will do this in reverse to split a single fraction into separate fractions.<\/p>\n<p id=\"fs-id1169597555516\">We\u2019ll state the fraction addition property here just as you learned it and in reverse.<\/p>\n\n<div id=\"fs-id1169597702997\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Fraction Addition<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597576926\">If \\(a,b\\), and \\(c\\) are numbers where \\(c\\ne 0\\), then<\/p>\n\n<div id=\"fs-id1169597364210\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\dfrac{a}{c}+\\dfrac{b}{c}=\\dfrac{a+b}{c}\\) and \\(\\dfrac{a+b}{c}=\\dfrac{a}{c}+\\dfrac{b}{c}\\)<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597394144\">We use the form on the left to add fractions and we use the form on the right to divide a polynomial by a monomial.<\/p>\n\n<table id=\"eip-657\" summary=\".\">\n<tbody>\n<tr>\n<td>For example,<\/td>\n<td>\\(\\dfrac{y+2}{5}\\)<\/td>\n<\/tr>\n<tr>\n<td>can be written<\/td>\n<td>\\(\\dfrac{y}{5}+\\dfrac{2}{5}\\).<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597334694\">We use this form of fraction addition to divide polynomials by monomials.<\/p>\n\n<div id=\"fs-id1169597491344\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Division of a Polynomial by a Monomial<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nTo divide a polynomial by a monomial, divide each term of the polynomial by the <span class=\"no-emphasis\" data-type=\"term\">monomial<\/span>.\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597466487\" data-type=\"problem\">\n<p id=\"fs-id1169597381554\">Find the quotient: \\(\\dfrac{7{y}^{2}+21}{7}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597531097\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-958\" class=\"unnumbered unstyled\" style=\"height: 58px\" summary=\".\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"height: 14px;width: 276.406px\"><\/td>\n<td style=\"height: 14px;width: 204.406px\">\\(\\dfrac{7{y}^{2}+21}{7}\\)<\/td>\n<\/tr>\n<tr style=\"height: 30px\">\n<td style=\"height: 30px;width: 276.406px\">Divide each term of the numerator by the denominator.<\/td>\n<td style=\"height: 30px;width: 204.406px\">\\(\\dfrac{7{y}^{2}}{7}+\\dfrac{21}{7}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"height: 14px;width: 276.406px\">Simplify each fraction.<\/td>\n<td style=\"height: 14px;width: 204.406px\">\\({y}^{2}+3\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597414519\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597366844\" data-type=\"exercise\">\n<div id=\"fs-id1169597494486\" data-type=\"problem\">\n<p id=\"fs-id1169597518761\">Find the quotient: \\(\\dfrac{8{z}^{2}+24}{4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597383953\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597344110\">\\(2{z}^{2}+6\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597576300\" data-type=\"problem\">\n<p id=\"fs-id1169597579154\">Find the quotient: \\(\\dfrac{18{z}^{2}-27}{9}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597379980\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597537992\">\\(2{z}^{2}-3\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597495783\">Remember that division can be represented as a fraction. When you are asked to divide a polynomial by a monomial and it is not already in fraction form, write a fraction with the polynomial in the numerator and the monomial in the denominator.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597395518\" data-type=\"problem\">\n<p id=\"fs-id1169597360676\">Find the quotient: \\(\\left(18{x}^{3}-36{x}^{2}\\right)\\div 6x\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597493630\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-560\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\left(18{x}^{3}-36{x}^{2}\\right)\\div 6x\\)<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a fraction.<\/td>\n<td>\\(\\dfrac{18{x}^{3}-36{x}^{2}}{6x}\\)<\/td>\n<\/tr>\n<tr>\n<td>Divide each term of the numerator by the denominator.<\/td>\n<td>\\(\\dfrac{18{x}^{3}}{6x}-\\dfrac{36{x}^{2}}{6x}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(3{x}^{2}-6x\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597457327\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597364029\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169597485217\">Find the quotient: \\(\\left(27{b}^{3}-33{b}^{2}\\right)\\div 3b\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597337165\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597381277\">\\(9{b}^{2}-11b\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597380989\" data-type=\"problem\">\n<p id=\"fs-id1169597421768\">Find the quotient: \\(\\left(25{y}^{3}-55{y}^{2}\\right)\\div 5y\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597460742\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597507210\">\\(5{y}^{2}-11y\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597494726\">When we divide by a negative, we must be extra careful with the signs.<\/p>\n\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597533874\" data-type=\"problem\">\n<p id=\"fs-id1169597492601\">Find the quotient: \\(\\dfrac{12{d}^{2}-16d}{-4}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597501851\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-992\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\dfrac{12{d}^{2}-16d}{-4}\\)<\/td>\n<\/tr>\n<tr>\n<td>Divide each term of the numerator by the denominator.<\/td>\n<td>\\(\\dfrac{12{d}^{2}}{-4}-\\dfrac{16d}{-4}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify. Remember, subtracting a negative is like adding a positive!<\/td>\n<td>\\(-3{d}^{2}+4d\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597394573\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597373652\" data-type=\"exercise\">\n<div id=\"fs-id1169597412822\" data-type=\"problem\">\n<p id=\"fs-id1169597352013\">Find the quotient: \\(\\dfrac{25{y}^{2}-15y}{-5}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597497900\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597415973\">\\(-5{y}^{2}+3y\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597386661\" data-type=\"problem\">\n<p id=\"fs-id1169597388331\">Find the quotient: \\(\\dfrac{42{b}^{2}-18b}{-6}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597514405\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597342466\">\\(-7{b}^{2}+3b\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597518545\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597380965\" data-type=\"exercise\">\n<div id=\"fs-id1169597514405\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597540593\" data-type=\"problem\">\n<p id=\"fs-id1169597500832\">Find the quotient: \\(\\dfrac{105{y}^{5}+75{y}^{3}}{5{y}^{2}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597415544\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-78\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\dfrac{105{y}^{5}+75{y}^{3}}{5{y}^{2}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Separate the terms.<\/td>\n<td>\\(\\dfrac{105{y}^{5}}{5{y}^{2}}+\\dfrac{75{y}^{3}}{5{y}^{2}}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(21{y}^{3}+15y\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597410664\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597513321\" data-type=\"exercise\">\n<div id=\"fs-id1169597401022\" data-type=\"problem\">\n<p id=\"fs-id1169597333321\">Find the quotient: \\(\\dfrac{60{d}^{7}+24{d}^{5}}{4{d}^{3}}\\).<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597495416\">\\(15{d}^{4}+6{d}^{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597387876\" data-type=\"problem\">\n<p id=\"fs-id1169597467170\">Find the quotient: \\(\\dfrac{216{p}^{7}-48{p}^{5}}{6{p}^{3}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597389499\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597408774\">\\(36{p}^{4}-8{p}^{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597388034\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597460151\" data-type=\"exercise\">\n<div id=\"fs-id1169597389499\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597527007\" data-type=\"problem\">\n<p id=\"fs-id1169597505361\">Find the quotient: \\(\\left(15{x}^{3}y-35x{y}^{2}\\right)\\div \\left(-5xy\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597514617\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-802\" class=\"unnumbered unstyled\" summary=\"\/\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\left(15{x}^{3}y-35x{y}^{2}\\right)\\div \\left(-5xy\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a fraction.<\/td>\n<td>\\(\\dfrac{15{x}^{3}y-35x{y}^{2}}{-5xy}\\)<\/td>\n<\/tr>\n<tr>\n<td>Separate the terms.<\/td>\n<td>\\(\\dfrac{15{x}^{3}y}{-5xy}-\\dfrac{35x{y}^{2}}{-5xy}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(-3{x}^{2}+7y\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597460197\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597393585\" data-type=\"exercise\">\n<div id=\"fs-id1169597699122\" data-type=\"problem\">\n<p id=\"fs-id1169597480855\">Find the quotient: \\(\\left(32{a}^{2}b-16a{b}^{2}\\right)\\div\\left(-8ab\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597498291\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597388358\">\\(-4a+2b\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597383472\" data-type=\"problem\">\n<p id=\"fs-id1169597380957\">Find the quotient: \\(\\left(-48{a}^{8}{b}^{4}-36{a}^{6}{b}^{5}\\right)\\div \\left(-6{a}^{3}{b}^{3}\\right)\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597492222\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597492224\">\\(8{a}^{5}b+6{a}^{3}{b}^{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597431912\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597338852\" data-type=\"exercise\">\n<div id=\"fs-id1169597492222\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597536289\" data-type=\"problem\">\n<p id=\"fs-id1169597536291\">Find the quotient: \\(\\dfrac{36{x}^{3}{y}^{2}+27{x}^{2}{y}^{2}-9{x}^{2}{y}^{3}}{9{x}^{2}y}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597445753\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-917\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\dfrac{36{x}^{3}{y}^{2}+27{x}^{2}{y}^{2}-9{x}^{2}{y}^{3}}{9{x}^{2}y}\\)<\/td>\n<\/tr>\n<tr>\n<td>Separate the terms.<\/td>\n<td>\\(\\dfrac{36{x}^{3}{y}^{2}}{9{x}^{2}y}+\\dfrac{27{x}^{2}{y}^{2}}{9{x}^{2}y}-\\dfrac{9{x}^{2}{y}^{3}}{9{x}^{2}y}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(4xy+3y-{y}^{2}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n&nbsp;\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597461002\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597687906\" data-type=\"exercise\">\n<div id=\"fs-id1169597687908\" data-type=\"problem\">\n<p id=\"fs-id1169597517317\">Find the quotient: \\(\\dfrac{40{x}^{3}{y}^{2}+24{x}^{2}{y}^{2}-16{x}^{2}{y}^{3}}{8{x}^{2}y}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597466727\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597507457\">\\(5xy+3y-2{y}^{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597380051\" data-type=\"problem\">\n<p id=\"fs-id1169597519110\">Find the quotient: \\(\\dfrac{35{a}^{4}{b}^{2}+14{a}^{4}{b}^{3}-42{a}^{2}{b}^{4}}{7{a}^{2}{b}^{2}}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597468109\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597468111\">\\(5{a}^{2}+2{a}^{2}b-6{b}^{2}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597497473\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597380049\" data-type=\"exercise\">\n<div id=\"fs-id1169597468109\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597539295\" data-type=\"problem\">\n<p id=\"fs-id1169597539514\">Find the quotient: \\(\\dfrac{10{x}^{2}+5x-20}{5x}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597538674\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-848\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>\\(\\dfrac{10{x}^{2}+5x-20}{5x}\\)<\/td>\n<\/tr>\n<tr>\n<td>Separate the terms.<\/td>\n<td>\\(\\dfrac{10{x}^{2}}{5x}+\\dfrac{5x}{5x}-\\dfrac{20}{5x}\\)<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>\\(2x+1+\\dfrac{4}{x}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597700078\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597700081\" data-type=\"exercise\">\n<div id=\"fs-id1169597525470\" data-type=\"problem\">\n<p id=\"fs-id1169597525472\">Find the quotient: \\(\\dfrac{18{c}^{2}+6c-9}{6c}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597481131\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597481133\">\\(3c+1-\\dfrac{3}{2c}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597576435\" data-type=\"problem\">\n<p id=\"fs-id1169597480452\">Find the quotient: \\(\\dfrac{10{d}^{2}-5d-2}{5d}\\).<\/p>\n\n<\/div>\n<div id=\"fs-id1169597691492\" data-type=\"solution\"><details><summary>Show answer<\/summary>\n<p id=\"fs-id1169597691494\">\\(2d-1-\\dfrac{2}{5d}\\)<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597340263\" class=\"media-2\" data-type=\"note\">\n<p id=\"fs-id1169597340267\">Access these online resources for additional instruction and practice with dividing polynomials:<\/p>\n\n<ul id=\"fs-id1169597340270\" data-display=\"block\">\n \t<li><a href=\"https:\/\/openstax.org\/l\/25DividePolyMo1\">Divide a Polynomial by a Monomial<\/a><\/li>\n \t<li><a href=\"https:\/\/openstax.org\/l\/25DividePolyMo2\">Divide a Polynomial by a Monomial 2<\/a><\/li>\n<\/ul>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1169597536569\" data-bullet-style=\"bullet\">\n \t<li><strong data-effect=\"bold\">Fraction Addition<\/strong>\n<ul id=\"fs-id1169597528209\" data-bullet-style=\"open-circle\">\n \t<li>If \\(a,b\\), and \\(c\\) are numbers where \\(c\\ne 0\\), then\n\\(\\dfrac{a}{c}+\\dfrac{b}{c}=\\dfrac{a+b}{c}\\) and \\(\\dfrac{a+b}{c}=\\frac{a}{c}+\\dfrac{b}{c}\\)<\/li>\n<\/ul>\n<\/li>\n \t<li><strong data-effect=\"bold\">Division of a Polynomial by a Monomial<\/strong>\n<ul id=\"fs-id1169597689368\" data-bullet-style=\"open-circle\">\n \t<li>To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Dividing Polynomial by Monomial<\/h2>\nIn the following exercises, divide each polynomial by the monomial.\n<table style=\"border-collapse: collapse;width: 100%;height: 196px\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">1. \\(\\frac{30b+75}{5}\\)<\/td>\n<td style=\"width: 50%;height: 14px\">2.\\(\\frac{45y+36}{9}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">3. \\(\\frac{42{x}^{2}-14x}{7}\\)<\/td>\n<td style=\"width: 50%;height: 14px\">4. \\(\\frac{8{d}^{2}-4d}{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">5. \\(\\left(55{w}^{2}-10w\\right)\\div5w\\)<\/td>\n<td style=\"width: 50%;height: 14px\">6. \\(\\left(16{y}^{2}-20y\\right)\\div4y\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">7. \\(\\left(8{x}^{3}+6{x}^{2}\\right)\\div2x\\)<\/td>\n<td style=\"width: 50%;height: 14px\">8. \\(\\left(9{n}^{4}+6{n}^{3}\\right)\\div3n\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">9. \\(\\frac{20{b}^{2}-12b}{-4}\\)<\/td>\n<td style=\"width: 50%;height: 14px\">10. \\(\\frac{18{y}^{2}-12y}{-6}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">11. \\(\\frac{51{m}^{4}+72{m}^{3}}{-3}\\)<\/td>\n<td style=\"width: 50%;height: 14px\">12. \\(\\frac{35{a}^{4}+65{a}^{2}}{-5}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">13. \\(\\frac{412{z}^{8}-48{z}^{5}}{4{z}^{3}}\\)<\/td>\n<td style=\"width: 50%;height: 14px\">14. \\(\\frac{310{y}^{4}-200{y}^{3}}{5{y}^{2}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">15. \\(\\frac{51{y}^{4}+42{y}^{2}}{3{y}^{2}}\\)<\/td>\n<td style=\"width: 50%;height: 14px\">16. \\(\\frac{46{x}^{3}+38{x}^{2}}{2{x}^{2}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">17. \\(\\left(35{x}^{4}-21x\\right)\\div \\left(-7x\\right)\\)<\/td>\n<td style=\"width: 50%;height: 14px\">18. \\(\\left(24{p}^{2}-33p\\right)\\div \\left(-3p\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">19. \\(\\left(48{y}^{4}-24{y}^{3}\\right)\\div \\left(-8{y}^{2}\\right)\\)<\/td>\n<td style=\"width: 50%;height: 14px\">20. \\(\\left(63{m}^{4}-42{m}^{3}\\right)\\div \\left(-7{m}^{2}\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">21. \\(\\left(45{x}^{3}{y}^{4}+60x{y}^{2}\\right)\\div \\left(5xy\\right)\\)<\/td>\n<td style=\"width: 50%;height: 14px\">22. \\(\\left(63{a}^{2}{b}^{3}+72a{b}^{4}\\right)\\div \\left(9ab\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">23. \\(\\frac{49{c}^{2}{d}^{2}-70{c}^{3}{d}^{3}-35{c}^{2}{d}^{4}}{7c{d}^{2}}\\)<\/td>\n<td style=\"width: 50%;height: 14px\">24. \\(\\frac{52{p}^{5}{q}^{4}+36{p}^{4}{q}^{3}-64{p}^{3}{q}^{2}}{4{p}^{2}q}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">25. \\(\\frac{72{r}^{5}{s}^{2}+132{r}^{4}{s}^{3}-96{r}^{3}{s}^{5}}{12{r}^{2}{s}^{2}}\\)<\/td>\n<td style=\"width: 50%;height: 14px\">26. \\(\\frac{66{x}^{3}{y}^{2}-110{x}^{2}{y}^{3}-44{x}^{4}{y}^{3}}{11{x}^{2}{y}^{2}}\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">27. \\(\\frac{12{q}^{2}+3q-1}{3q}\\)<\/td>\n<td style=\"width: 50%;height: 14px\">28. \\(\\frac{4{w}^{2}+2w-5}{2w}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">29. \\(\\frac{20{y}^{2}+12y-1}{-4y}\\)<\/td>\n<td style=\"width: 50%\">30. \\(\\frac{10{x}^{2}+5x-4}{-5x}\\)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">31. \\(\\frac{63{a}^{3}-108{a}^{2}+99a}{9{a}^{2}}\\)<\/td>\n<td style=\"width: 50%\">32. \\(\\frac{36{p}^{3}+18{p}^{2}-12p}{6{p}^{2}}\\)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Everyday Math<\/h2>\n<div id=\"fs-id1169597517358\" data-type=\"problem\">\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 49.8159%\">33. Handshakes At a company meeting, every employee shakes hands with every other employee. The number of handshakes is given by the expression \\(\\frac{{n}^{2}-n}{2}\\), where \\(n\\) represents the number of employees. How many handshakes will there be if there are 10 employees at the meeting?<\/td>\n<td style=\"width: 50.0614%\">\n<p id=\"fs-id1169597533048\">34. Average cost Pictures Plus produces digital albums. The company\u2019s average cost (in dollars) to make \\(x\\) albums is given by the expression \\(\\frac{7x+500}{x}\\).<\/p>\n\n<ol id=\"fs-id1168745404763\" type=\"a\">\n \t<li>Find the quotient by dividing the numerator by the denominator.<\/li>\n \t<li>What will the average cost (in dollars) be to produce 20 albums?<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">35. Divide \\(\\frac{10{x}^{2}+x-12}{2x}\\) and explain with words how you get each term of the quotient.<\/td>\n<td style=\"width: 50%\">36. James divides \\(48y+6\\) by 6 this way: \\(\\frac{48y+\\overline{)6}}{\\overline{)6}}=48y\\). What is wrong with his reasoning?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse;width: 100%;height: 160px\" border=\"0\">\n<tbody>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">1. \\(6b+15\\)<\/td>\n<td style=\"width: 33.3333%;height: 16px\">3. \\(6{x}^{2}-2x\\)<\/td>\n<td style=\"width: 33.3333%;height: 16px\">5. \\(11w-2\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">7. \\(4{x}^{2}+3x\\)<\/td>\n<td style=\"width: 33.3333%;height: 16px\">9. \\(-5{b}^{2}+3b\\)<\/td>\n<td style=\"width: 33.3333%;height: 16px\">11.\u00a0\\(-17{m}^{4}-24{m}^{3}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">13. \\(103{z}^{5}-12{z}^{2}\\)<\/td>\n<td style=\"width: 33.3333%;height: 16px\">15. \\(17{y}^{2}+14\\)<\/td>\n<td style=\"width: 33.3333%;height: 16px\">17. \\(-5{x}^{3}+3\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">19. \\(-6{y}^{2}+3y\\)<\/td>\n<td style=\"width: 33.3333%;height: 16px\">21. \\(9{x}^{2}{y}^{3}+12y\\)<\/td>\n<td style=\"width: 33.3333%;height: 16px\">23. \\(7c-10{c}^{2}d-5c{d}^{2}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">25. \\(6{r}^{3}+11{r}^{2}s-8r{s}^{3}\\)<\/td>\n<td style=\"width: 33.3333%;height: 16px\">27. \\(4q+1-\\frac{1}{3q}\\)<\/td>\n<td style=\"width: 33.3333%;height: 16px\">29. \\(-5y-3+\\frac{1}{4y}\\)<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">31. \\(7a-12+\\frac{11}{a}\\)<\/td>\n<td style=\"width: 33.3333%;height: 16px\">33. 45<\/td>\n<td style=\"width: 33.3333%;height: 16px\">35.\u00a0Answers will vary.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\nThis chapter has been adapted from \u201cDivide Polynomials\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.\u00a0<!-- pb_fixme -->","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Divide a polynomial by a monomial<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Divide a Polynomial by a Monomial<\/h1>\n<p id=\"fs-id1169597495901\">In the last chapter, you learned how to divide a monomial by a monomial. As you continue to build up your knowledge of polynomials the next procedure is to divide a polynomial of two or more terms by a <span class=\"no-emphasis\" data-type=\"term\">monomial<\/span>.<\/p>\n<p id=\"fs-id1169597414468\">The method we\u2019ll use to divide a polynomial by a monomial is based on the properties of fraction addition. So we\u2019ll start with an example to review fraction addition.<\/p>\n<table id=\"eip-903\" summary=\".\">\n<tbody>\n<tr>\n<td>The sum,<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4c60c777ed1a90a81c81425fdaa8a149_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#121;&#125;&#123;&#53;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"44\" style=\"vertical-align: -12px;\" \/>,<\/td>\n<\/tr>\n<tr>\n<td>simplifies to<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2064e2a213a68b6cf32dbdce3393bf93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#121;&#43;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"40\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597690628\">Now we will do this in reverse to split a single fraction into separate fractions.<\/p>\n<p id=\"fs-id1169597555516\">We\u2019ll state the fraction addition property here just as you learned it and in reverse.<\/p>\n<div id=\"fs-id1169597702997\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Fraction Addition<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1169597576926\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c8f07275913233044208899fc485a8ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-77479b59a494b611004da289deb0dfa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> are numbers where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bed56f875d4ad7cd58cfe6766f834124_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/>, then<\/p>\n<div id=\"fs-id1169597364210\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d881a41accff42d94020ee28e231dd6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#43;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"109\" style=\"vertical-align: -12px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-161cf01bca5c9fd9814a1b6940002ff0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#43;&#98;&#125;&#123;&#99;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"109\" style=\"vertical-align: -12px;\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597394144\">We use the form on the left to add fractions and we use the form on the right to divide a polynomial by a monomial.<\/p>\n<table id=\"eip-657\" summary=\".\">\n<tbody>\n<tr>\n<td>For example,<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2064e2a213a68b6cf32dbdce3393bf93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#121;&#43;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"40\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>can be written<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4c60c777ed1a90a81c81425fdaa8a149_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#121;&#125;&#123;&#53;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"44\" style=\"vertical-align: -12px;\" \/>.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1169597334694\">We use this form of fraction addition to divide polynomials by monomials.<\/p>\n<div id=\"fs-id1169597491344\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Division of a Polynomial by a Monomial<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>To divide a polynomial by a monomial, divide each term of the polynomial by the <span class=\"no-emphasis\" data-type=\"term\">monomial<\/span>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597466487\" data-type=\"problem\">\n<p id=\"fs-id1169597381554\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-27d9d131611cf20417ddcd1c984c138f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#49;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"66\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597531097\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-958\" class=\"unnumbered unstyled\" style=\"height: 58px\" summary=\".\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"height: 14px;width: 276.406px\"><\/td>\n<td style=\"height: 14px;width: 204.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-27d9d131611cf20417ddcd1c984c138f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#49;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"66\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 30px\">\n<td style=\"height: 30px;width: 276.406px\">Divide each term of the numerator by the denominator.<\/td>\n<td style=\"height: 30px;width: 204.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7a0387ce2b112673fcff6e4b18b72ebe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#55;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#49;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"69\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"height: 14px;width: 276.406px\">Simplify each fraction.<\/td>\n<td style=\"height: 14px;width: 204.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5de2accc01c24c810792f8d9a7acfea5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"48\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597414519\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597366844\" data-type=\"exercise\">\n<div id=\"fs-id1169597494486\" data-type=\"problem\">\n<p id=\"fs-id1169597518761\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0565fd78c246fb82b799d6d205e45bc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#56;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#52;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"65\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597383953\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597344110\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c65f01df9bf31ff1076f4f0778031140_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"56\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597576300\" data-type=\"problem\">\n<p id=\"fs-id1169597579154\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-692e951781946ec05e5a5bbd5e55c086_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#55;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"74\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597379980\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597537992\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-695175c529f5417911fd6c058a973f3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#122;&#125;&#94;&#123;&#50;&#125;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597495783\">Remember that division can be represented as a fraction. When you are asked to divide a polynomial by a monomial and it is not already in fraction form, write a fraction with the polynomial in the numerator and the monomial in the denominator.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597395518\" data-type=\"problem\">\n<p id=\"fs-id1169597360676\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9ff2c20a1df6bb1512ff6a4e2a693c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#51;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"148\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597493630\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-560\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d9ff2c20a1df6bb1512ff6a4e2a693c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#51;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"148\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a fraction.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-71032434a775df092d8d1996bfedc8d5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#45;&#51;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#54;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"93\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide each term of the numerator by the denominator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-04b80667550a782441e65bccccf92b93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#54;&#120;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#54;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"97\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0aaf8ada10ca6b74e6ed22ff49fef674_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#54;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"67\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597457327\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597364029\" data-type=\"exercise\">\n<div data-type=\"problem\">\n<p id=\"fs-id1169597485217\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7705e7b5bb56e8f049306f385e5d1207_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#55;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#45;&#51;&#51;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#51;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"141\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597337165\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597381277\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-12629ed4289cbc21f3f3fcc9d14c6a66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#49;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"72\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597380989\" data-type=\"problem\">\n<p id=\"fs-id1169597421768\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-21ccde11b23814cd4e3a1e73391fdd31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#53;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#53;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"145\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597460742\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597507210\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-540886d0a97d79b6fabb4d932363f94f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#49;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1169597494726\">When we divide by a negative, we must be extra careful with the signs.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597533874\" data-type=\"problem\">\n<p id=\"fs-id1169597492601\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fd6f1c5a15015678d95c31c7b681a199_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#54;&#100;&#125;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"84\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597501851\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-992\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-fd6f1c5a15015678d95c31c7b681a199_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#54;&#100;&#125;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"84\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide each term of the numerator by the denominator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ac5d0e897353791d0e9d036fc7f8fadb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#45;&#52;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#54;&#100;&#125;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"88\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify. Remember, subtracting a negative is like adding a positive!<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-16595faa8e82aa3b4fcfbe667436cc36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#43;&#52;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"79\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597394573\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597373652\" data-type=\"exercise\">\n<div id=\"fs-id1169597412822\" data-type=\"problem\">\n<p id=\"fs-id1169597352013\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2c14de95f930c00ba69825b91c5a075d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#53;&#121;&#125;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"84\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597497900\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597415973\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-85e058123fc147294adfd6f24dfe31c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597386661\" data-type=\"problem\">\n<p id=\"fs-id1169597388331\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d48862770d61a6fe56985110bcb1ddc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#50;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#56;&#98;&#125;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"81\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597514405\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597342466\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-679435c071ddbc8f4c999471db49b491_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"76\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597518545\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597380965\" data-type=\"exercise\">\n<div id=\"fs-id1169597514405\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597540593\" data-type=\"problem\">\n<p id=\"fs-id1169597500832\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-42fe375cce8188f2aaa5b1057f3edeb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#53;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#43;&#55;&#53;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"101\" style=\"vertical-align: -16px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597415544\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-78\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-42fe375cce8188f2aaa5b1057f3edeb8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#53;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#43;&#55;&#53;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"101\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Separate the terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c75595146029018a53401dbda37b218a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#53;&#123;&#121;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#55;&#53;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"104\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-86a11d0d9ec333586b80bac9f708237b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#43;&#49;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597410664\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597513321\" data-type=\"exercise\">\n<div id=\"fs-id1169597401022\" data-type=\"problem\">\n<p id=\"fs-id1169597333321\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9b830d7d10766427c786f2a25f560c20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#54;&#48;&#123;&#100;&#125;&#94;&#123;&#55;&#125;&#43;&#50;&#52;&#123;&#100;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#52;&#123;&#100;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"91\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597495416\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a2aa98f09f44f73745e24eb0a896f201_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#123;&#100;&#125;&#94;&#123;&#52;&#125;&#43;&#54;&#123;&#100;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"80\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597387876\" data-type=\"problem\">\n<p id=\"fs-id1169597467170\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9eb85872a23e62ddaf115adbb57cf7b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#49;&#54;&#123;&#112;&#125;&#94;&#123;&#55;&#125;&#45;&#52;&#56;&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#54;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"100\" style=\"vertical-align: -16px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597389499\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597408774\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d423567f3533ae8743754606b2814283_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#45;&#56;&#123;&#112;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597388034\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597460151\" data-type=\"exercise\">\n<div id=\"fs-id1169597389499\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597527007\" data-type=\"problem\">\n<p id=\"fs-id1169597505361\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0c559eb78fc39b2155a417dbc835a105_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;&#45;&#51;&#53;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#120;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"202\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597514617\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-802\" class=\"unnumbered unstyled\" summary=\"\/\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-0c559eb78fc39b2155a417dbc835a105_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;&#45;&#51;&#53;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#120;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"202\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a fraction.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4cdcb666d17689ad1c6ff3a4de6bb109_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;&#45;&#51;&#53;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#45;&#53;&#120;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"112\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Separate the terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bbf60352c09341549937eeba460a0277_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#121;&#125;&#123;&#45;&#53;&#120;&#121;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#53;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#45;&#53;&#120;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"115\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d7e0db24a2b3ef0c7f25cd9546f500fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#55;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"79\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597460197\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597393585\" data-type=\"exercise\">\n<div id=\"fs-id1169597699122\" data-type=\"problem\">\n<p id=\"fs-id1169597480855\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-a00034bd72cc5ca086bf7bb018278964_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#50;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#45;&#49;&#54;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#97;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"195\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597498291\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597388358\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-04306fd089253196cb60b2910d4e1263_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#97;&#43;&#50;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"70\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597383472\" data-type=\"problem\">\n<p id=\"fs-id1169597380957\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-908ae14a1692333a08003521af7f5e90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#56;&#123;&#97;&#125;&#94;&#123;&#56;&#125;&#123;&#98;&#125;&#94;&#123;&#52;&#125;&#45;&#51;&#54;&#123;&#97;&#125;&#94;&#123;&#54;&#125;&#123;&#98;&#125;&#94;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#54;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"241\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597492222\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597492224\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7d359553e7a20a183b021fe09b6c4e2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#97;&#125;&#94;&#123;&#53;&#125;&#98;&#43;&#54;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"96\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597431912\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597338852\" data-type=\"exercise\">\n<div id=\"fs-id1169597492222\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597536289\" data-type=\"problem\">\n<p id=\"fs-id1169597536291\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d2bce19c87eb1cd957a697e750a3ba63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#54;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"193\" style=\"vertical-align: -16px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597445753\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-917\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d2bce19c87eb1cd957a697e750a3ba63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#54;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"193\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Separate the terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5d03e731efbd9f56964778a505842620_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#54;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#55;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"200\" style=\"vertical-align: -16px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8329ece48f2b8d5a558cba3f6bd34016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#121;&#43;&#51;&#121;&#45;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597461002\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597687906\" data-type=\"exercise\">\n<div id=\"fs-id1169597687908\" data-type=\"problem\">\n<p id=\"fs-id1169597517317\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-01cb5675d96d7d07cd86726bc20b2971_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#48;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"202\" style=\"vertical-align: -16px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597466727\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597507457\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-55561ef2d201d006a4eddb4450ece688_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#121;&#43;&#51;&#121;&#45;&#50;&#123;&#121;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"115\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597380051\" data-type=\"problem\">\n<p id=\"fs-id1169597519110\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-45bc4475fd4c8c90b603d5cc1bb9d6e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#53;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#52;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#45;&#52;&#50;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#55;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"194\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597468109\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597468111\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-82fcf2b20927814bbb04068b3a9e04d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#98;&#45;&#54;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"127\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597497473\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597380049\" data-type=\"exercise\">\n<div id=\"fs-id1169597468109\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597539295\" data-type=\"problem\">\n<p id=\"fs-id1169597539514\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-30090e5d4b732ae4f110e6f72bed0f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#45;&#50;&#48;&#125;&#123;&#53;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"116\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597538674\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-848\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-30090e5d4b732ae4f110e6f72bed0f58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#45;&#50;&#48;&#125;&#123;&#53;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"116\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Separate the terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-dc298740b728a12bfed01a6091beb9d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#53;&#120;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#53;&#120;&#125;&#123;&#53;&#120;&#125;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#48;&#125;&#123;&#53;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"125\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4021f1aa7856822d3ea04c0e20d3e3b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#43;&#49;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"84\" style=\"vertical-align: -12px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597700078\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1169597700081\" data-type=\"exercise\">\n<div id=\"fs-id1169597525470\" data-type=\"problem\">\n<p id=\"fs-id1169597525472\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-b22a708df04db1e50e5eafd2fc54c9a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#43;&#54;&#99;&#45;&#57;&#125;&#123;&#54;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"102\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597481131\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597481133\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3c0b64850f146c3b328be6c7c823a298_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#99;&#43;&#49;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"88\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1169597576435\" data-type=\"problem\">\n<p id=\"fs-id1169597480452\">Find the quotient: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-22b8be35c6096b6636959193a469ec83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#45;&#53;&#100;&#45;&#50;&#125;&#123;&#53;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"105\" style=\"vertical-align: -12px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1169597691492\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1169597691494\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ef034dcc475636adce37f8ef0f3b6dc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#100;&#45;&#49;&#45;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"91\" style=\"vertical-align: -12px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1169597340263\" class=\"media-2\" data-type=\"note\">\n<p id=\"fs-id1169597340267\">Access these online resources for additional instruction and practice with dividing polynomials:<\/p>\n<ul id=\"fs-id1169597340270\" data-display=\"block\">\n<li><a href=\"https:\/\/openstax.org\/l\/25DividePolyMo1\">Divide a Polynomial by a Monomial<\/a><\/li>\n<li><a href=\"https:\/\/openstax.org\/l\/25DividePolyMo2\">Divide a Polynomial by a Monomial 2<\/a><\/li>\n<\/ul>\n<\/div>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1169597536569\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Fraction Addition<\/strong>\n<ul id=\"fs-id1169597528209\" data-bullet-style=\"open-circle\">\n<li>If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c8f07275913233044208899fc485a8ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-77479b59a494b611004da289deb0dfa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> are numbers where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bed56f875d4ad7cd58cfe6766f834124_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/>, then<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d881a41accff42d94020ee28e231dd6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;&#61;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#43;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"109\" style=\"vertical-align: -12px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c00cd512fa1c64818f8b59c9f9845da9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#43;&#98;&#125;&#123;&#99;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#43;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"107\" style=\"vertical-align: -12px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Division of a Polynomial by a Monomial<\/strong>\n<ul id=\"fs-id1169597689368\" data-bullet-style=\"open-circle\">\n<li>To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Dividing Polynomial by Monomial<\/h2>\n<p>In the following exercises, divide each polynomial by the monomial.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 196px\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ac21501e04ed38eba56e76aafdba20ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#48;&#98;&#43;&#55;&#53;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"45\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">2.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c7345da8b4793c702f8163cfebba64d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#53;&#121;&#43;&#51;&#54;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"46\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-afbb62b2809606a2c88152ff42b45b76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#52;&#120;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"61\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3c3fd45a98d5aea7edaf81e983e5eb89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#45;&#52;&#100;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"47\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1a44282d2b28bf2b733451dba0122fb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#53;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#48;&#119;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#53;&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"149\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-f864a29e7c9ee9963432fcac188acfbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#48;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#52;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"137\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bf1963373489b5a5d34a95ec56f20542_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"130\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6fa461c335540a6a20f00cb26d763779_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#123;&#110;&#125;&#94;&#123;&#52;&#125;&#43;&#54;&#123;&#110;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#51;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"132\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-785acb65cacebf10c27cc29b7df0dff8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#48;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#50;&#98;&#125;&#123;&#45;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d8bf9d6e9aa048f548bcb76bb3e3b205_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#50;&#121;&#125;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"60\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4fe2d68b7c6486cb5bceed93ec795072_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#49;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#43;&#55;&#50;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#45;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"77\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d409d5545eb344d7508fa2753ce14d17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#53;&#123;&#97;&#125;&#94;&#123;&#52;&#125;&#43;&#54;&#53;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"67\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-2b10a1a8058567de0995e493dfad5e29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#49;&#50;&#123;&#122;&#125;&#94;&#123;&#56;&#125;&#45;&#52;&#56;&#123;&#122;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#52;&#123;&#122;&#125;&#94;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"73\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-abfa0e06325bc05214b30b915369316d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#49;&#48;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#45;&#50;&#48;&#48;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#53;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"81\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4972d4bf664edc61c157ba931198f489_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#49;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#43;&#52;&#50;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#51;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"67\" style=\"vertical-align: -10px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3e348af5e7cc18ba004ced036191bbe3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#54;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#51;&#56;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"68\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-c6cdd0b26d02630bc27d5779ca2a3c45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#53;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#45;&#50;&#49;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"167\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8b1e97b63d06ff368cbed7da5596ae25_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#52;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#51;&#51;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"163\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d80a7c3b2421556ab6a66d590fc93bb2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#56;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#45;&#50;&#52;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"181\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-445bdae68ebff995e34880d7c7c6e2bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#51;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#45;&#52;&#50;&#123;&#109;&#125;&#94;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#123;&#109;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"200\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1e69f028152c695d20f8771f932a656e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#52;&#125;&#43;&#54;&#48;&#120;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#120;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"196\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-141b1d10b49d5a526db00cca39e4a373_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#51;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#123;&#98;&#125;&#94;&#123;&#51;&#125;&#43;&#55;&#50;&#97;&#123;&#98;&#125;&#94;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#97;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"189\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3d1f13a2a8683ae55bd19a014cf115ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#57;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#45;&#55;&#48;&#123;&#99;&#125;&#94;&#123;&#51;&#125;&#123;&#100;&#125;&#94;&#123;&#51;&#125;&#45;&#51;&#53;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#123;&#100;&#125;&#94;&#123;&#52;&#125;&#125;&#123;&#55;&#99;&#123;&#100;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"143\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-133e42bc375d4ea4ee799c229347f407_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#50;&#123;&#112;&#125;&#94;&#123;&#53;&#125;&#123;&#113;&#125;&#94;&#123;&#52;&#125;&#43;&#51;&#54;&#123;&#112;&#125;&#94;&#123;&#52;&#125;&#123;&#113;&#125;&#94;&#123;&#51;&#125;&#45;&#54;&#52;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#52;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"144\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-de971e3e910b51e7172e02225e98e22e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#50;&#123;&#114;&#125;&#94;&#123;&#53;&#125;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#51;&#50;&#123;&#114;&#125;&#94;&#123;&#52;&#125;&#123;&#115;&#125;&#94;&#123;&#51;&#125;&#45;&#57;&#54;&#123;&#114;&#125;&#94;&#123;&#51;&#125;&#123;&#115;&#125;&#94;&#123;&#53;&#125;&#125;&#123;&#49;&#50;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"149\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e13db46de19b81ce972f78299063bd75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#54;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#45;&#52;&#52;&#123;&#120;&#125;&#94;&#123;&#52;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#125;&#123;&#49;&#49;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"156\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-4d7c7ced370ee99c1f30acc71fe20fe0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#123;&#113;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#113;&#45;&#49;&#125;&#123;&#51;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"69\" style=\"vertical-align: -9px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-79d26f0c60ac416dc6d3ce2ca9f4b1bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#123;&#119;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#119;&#45;&#53;&#125;&#123;&#50;&#119;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"70\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bfc88bbb89046fe2d76f9f90fad7cef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#48;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#50;&#121;&#45;&#49;&#125;&#123;&#45;&#52;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"78\" style=\"vertical-align: -9px;\" \/><\/td>\n<td style=\"width: 50%\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-82f9a371e9ed4cae25ad956513401357_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#53;&#120;&#45;&#52;&#125;&#123;&#45;&#53;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"72\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d74e615abe439ee830402548e8849cda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#51;&#123;&#97;&#125;&#94;&#123;&#51;&#125;&#45;&#49;&#48;&#56;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#43;&#57;&#57;&#97;&#125;&#123;&#57;&#123;&#97;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"105\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-7c4f80cf59c035f3401e831d6349e0bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#54;&#123;&#112;&#125;&#94;&#123;&#51;&#125;&#43;&#49;&#56;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#45;&#49;&#50;&#112;&#125;&#123;&#54;&#123;&#112;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"30\" width=\"98\" style=\"vertical-align: -10px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Everyday Math<\/h2>\n<div id=\"fs-id1169597517358\" data-type=\"problem\">\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 49.8159%\">33. Handshakes At a company meeting, every employee shakes hands with every other employee. The number of handshakes is given by the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-3cefda7412e9efbf80ef3a91b1573476_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#110;&#125;&#94;&#123;&#50;&#125;&#45;&#110;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"35\" style=\"vertical-align: -6px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-1772f700b10cd40d7410781794beb211_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> represents the number of employees. How many handshakes will there be if there are 10 employees at the meeting?<\/td>\n<td style=\"width: 50.0614%\">\n<p id=\"fs-id1169597533048\">34. Average cost Pictures Plus produces digital albums. The company\u2019s average cost (in dollars) to make <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bb53ce30a3ff5b6ca87fc6e1eb6588a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> albums is given by the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6d5ef9125ac5592f6c87ca3a314a0ba6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#120;&#43;&#53;&#48;&#48;&#125;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"47\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<ol id=\"fs-id1168745404763\" type=\"a\">\n<li>Find the quotient by dividing the numerator by the denominator.<\/li>\n<li>What will the average cost (in dollars) be to produce 20 albums?<\/li>\n<\/ol>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">35. Divide <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-02ae161796582f2fe4a732cee4d844fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#120;&#45;&#49;&#50;&#125;&#123;&#50;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"72\" style=\"vertical-align: -6px;\" \/> and explain with words how you get each term of the quotient.<\/td>\n<td style=\"width: 50%\">36. James divides <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-310bc4f08d546d5fb078e10dd2d043ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#56;&#121;&#43;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"58\" style=\"vertical-align: -4px;\" \/> by 6 this way: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-288ae411bc7cfe9da1697c2855c4c021_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#56;&#121;&#43;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#54;&#125;&#125;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#54;&#125;&#125;&#61;&#52;&#56;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"96\" style=\"vertical-align: -13px;\" \/>. What is wrong with his reasoning?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<table style=\"border-collapse: collapse;width: 100%;height: 160px\">\n<tbody>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-ce1eec49c493dacf9e73c83785edb4c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#98;&#43;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-9e99e65b7f21b09f77241feee2363a2f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#45;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"67\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-8e7456cf684c62fe8598c61b7d81c05f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#119;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"60\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-58c1416a134c0f1d7c1827ca9b1d9306_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"67\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-e7b73adcb4ae22f4b5e0db05954a9f52_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#123;&#98;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"76\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">11.\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-961969529b83044ac59e0edb6946f759_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#55;&#123;&#109;&#125;&#94;&#123;&#52;&#125;&#45;&#50;&#52;&#123;&#109;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"116\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-19bfdd659953ef52a1bc27c496baa4aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#51;&#123;&#122;&#125;&#94;&#123;&#53;&#125;&#45;&#49;&#50;&#123;&#122;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"98\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-5ce162017fc3b3e25894e899e7f25b3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-98e2011ddb46023704a6fab04a0a6a47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#123;&#120;&#125;&#94;&#123;&#51;&#125;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"70\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-d917e1347f09f54ddb2bd93337fa2e56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#123;&#121;&#125;&#94;&#123;&#50;&#125;&#43;&#51;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-df03bfb637e335a3f5ec2dde5c4d3312_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;&#43;&#49;&#50;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-46edf5f791155fa1ad7b6bfb96d7e189_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#99;&#45;&#49;&#48;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#100;&#45;&#53;&#99;&#123;&#100;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"135\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-6e5a294b28a4c976543d371f7222070c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#123;&#114;&#125;&#94;&#123;&#51;&#125;&#43;&#49;&#49;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#115;&#45;&#56;&#114;&#123;&#115;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"143\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-96d6c4d80b4369aa473480256271aef6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#113;&#43;&#49;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"86\" style=\"vertical-align: -9px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-bf1e6d6b91e8c99a532aaa52f2b21ce7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#121;&#45;&#51;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"100\" style=\"vertical-align: -9px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math53\/wp-content\/ql-cache\/quicklatex.com-754d3cc1c50a783baf50258f530f563d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#97;&#45;&#49;&#50;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"95\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">33. 45<\/td>\n<td style=\"width: 33.3333%;height: 16px\">35.\u00a0Answers will vary.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cDivide Polynomials\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em> (OpenStax)<\/a> by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.\u00a0<!-- pb_fixme --><\/p>\n","protected":false},"author":999,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-1898","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":1647,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1898","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1898\/revisions"}],"predecessor-version":[{"id":1899,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1898\/revisions\/1899"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/parts\/1647"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapters\/1898\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/media?parent=1898"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/pressbooks\/v2\/chapter-type?post=1898"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/contributor?post=1898"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/math53\/wp-json\/wp\/v2\/license?post=1898"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}