{"id":319,"date":"2015-09-18T21:17:01","date_gmt":"2015-09-18T21:17:01","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=319"},"modified":"2015-11-04T17:24:19","modified_gmt":"2015-11-04T17:24:19","slug":"solutions-5","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/solutions-5\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"<h2>Solutions to Try Its<\/h2>\r\n1.\u00a0[latex]\\left({b}^{2}-a\\right)\\left(x+6\\right)[\/latex]\r\n\r\n2.\u00a0[latex]\\left(x - 6\\right)\\left(x - 1\\right)[\/latex]\r\n\r\n3. a. [latex]\\left(2x+3\\right)\\left(x+3\\right)[\/latex]\r\nb. [latex]\\left(3x - 1\\right)\\left(2x+1\\right)[\/latex]\r\n\r\n4.\u00a0[latex]{\\left(7x - 1\\right)}^{2}[\/latex]\r\n\r\n5.\u00a0[latex]\\left(9y+10\\right)\\left(9y - 10\\right)[\/latex]\r\n\r\n6.\u00a0[latex]\\left(6a+b\\right)\\left(36{a}^{2}-6ab+{b}^{2}\\right)[\/latex]\r\n\r\n7.\u00a0[latex]\\left(10x - 1\\right)\\left(100{x}^{2}+10x+1\\right)[\/latex]\r\n\r\n8.\u00a0[latex]{\\left(5a - 1\\right)}^{-\\frac{1}{4}}\\left(17a - 2\\right)[\/latex]\r\n<h2>Solutions to Odd-Numbered Exercises<\/h2>\r\n1.\u00a0The terms of a polynomial do not have to have a common factor for the entire polynomial to be factorable. For example, [latex]4{x}^{2}[\/latex] and [latex]-9{y}^{2}[\/latex] don\u2019t have a common factor, but the whole polynomial is still factorable: [latex]4{x}^{2}-9{y}^{2}=\\left(2x+3y\\right)\\left(2x - 3y\\right)[\/latex].\r\n\r\n3.\u00a0Divide the [latex]x[\/latex] term into the sum of two terms, factor each portion of the expression separately, and then factor out the GCF of the entire expression.\r\n\r\n5.\u00a0[latex]7m[\/latex]\r\n\r\n7.\u00a0[latex]10{m}^{3}[\/latex]\r\n\r\n9.\u00a0[latex]y[\/latex]\r\n\r\n11.\u00a0[latex]\\left(2a - 3\\right)\\left(a+6\\right)[\/latex]\r\n\r\n13.\u00a0[latex]\\left(3n - 11\\right)\\left(2n+1\\right)[\/latex]\r\n\r\n15.\u00a0[latex]\\left(p+1\\right)\\left(2p - 7\\right)[\/latex]\r\n\r\n17.\u00a0[latex]\\left(5h+3\\right)\\left(2h - 3\\right)[\/latex]\r\n\r\n19.\u00a0[latex]\\left(9d - 1\\right)\\left(d - 8\\right)[\/latex]\r\n\r\n21.\u00a0[latex]\\left(12t+13\\right)\\left(t - 1\\right)[\/latex]\r\n\r\n23.\u00a0[latex]\\left(4x+10\\right)\\left(4x - 10\\right)[\/latex]\r\n\r\n25.\u00a0[latex]\\left(11p+13\\right)\\left(11p - 13\\right)[\/latex]\r\n\r\n27.\u00a0[latex]\\left(19d+9\\right)\\left(19d - 9\\right)[\/latex]\r\n\r\n29.\u00a0[latex]\\left(12b+5c\\right)\\left(12b - 5c\\right)[\/latex]\r\n\r\n31.\u00a0[latex]{\\left(7n+12\\right)}^{2}[\/latex]\r\n\r\n33.\u00a0[latex]{\\left(15y+4\\right)}^{2}[\/latex]\r\n\r\n35.\u00a0[latex]{\\left(5p - 12\\right)}^{2}[\/latex]\r\n\r\n37.\u00a0[latex]\\left(x+6\\right)\\left({x}^{2}-6x+36\\right)[\/latex]\r\n\r\n39.\u00a0[latex]\\left(5a+7\\right)\\left(25{a}^{2}-35a+49\\right)[\/latex]\r\n\r\n41.\u00a0[latex]\\left(4x - 5\\right)\\left(16{x}^{2}+20x+25\\right)[\/latex]\r\n\r\n43.\u00a0[latex]\\left(5r+12s\\right)\\left(25{r}^{2}-60rs+144{s}^{2}\\right)[\/latex]\r\n\r\n45.\u00a0[latex]{\\left(2c+3\\right)}^{-\\frac{1}{4}}\\left(-7c - 15\\right)[\/latex]\r\n\r\n47.\u00a0[latex]{\\left(x+2\\right)}^{-\\frac{2}{5}}\\left(19x+10\\right)[\/latex]\r\n\r\n49.\u00a0[latex]{\\left(2z - 9\\right)}^{-\\frac{3}{2}}\\left(27z - 99\\right)[\/latex]\r\n\r\n51.\u00a0[latex]\\left(14x - 3\\right)\\left(7x+9\\right)[\/latex]\r\n\r\n53.\u00a0[latex]\\left(3x+5\\right)\\left(3x - 5\\right)[\/latex]\r\n\r\n55.\u00a0[latex]{\\left(2x+5\\right)}^{2}{\\left(2x - 5\\right)}^{2}[\/latex]\r\n\r\n57.\u00a0[latex]\\left(4{z}^{2}+49{a}^{2}\\right)\\left(2z+7a\\right)\\left(2z - 7a\\right)[\/latex]\r\n\r\n59.\u00a0[latex]\\frac{1}{\\left(4x+9\\right)\\left(4x - 9\\right)\\left(2x+3\\right)}[\/latex]","rendered":"<h2>Solutions to Try Its<\/h2>\n<p>1.\u00a0[latex]\\left({b}^{2}-a\\right)\\left(x+6\\right)[\/latex]<\/p>\n<p>2.\u00a0[latex]\\left(x - 6\\right)\\left(x - 1\\right)[\/latex]<\/p>\n<p>3. a. [latex]\\left(2x+3\\right)\\left(x+3\\right)[\/latex]<br \/>\nb. [latex]\\left(3x - 1\\right)\\left(2x+1\\right)[\/latex]<\/p>\n<p>4.\u00a0[latex]{\\left(7x - 1\\right)}^{2}[\/latex]<\/p>\n<p>5.\u00a0[latex]\\left(9y+10\\right)\\left(9y - 10\\right)[\/latex]<\/p>\n<p>6.\u00a0[latex]\\left(6a+b\\right)\\left(36{a}^{2}-6ab+{b}^{2}\\right)[\/latex]<\/p>\n<p>7.\u00a0[latex]\\left(10x - 1\\right)\\left(100{x}^{2}+10x+1\\right)[\/latex]<\/p>\n<p>8.\u00a0[latex]{\\left(5a - 1\\right)}^{-\\frac{1}{4}}\\left(17a - 2\\right)[\/latex]<\/p>\n<h2>Solutions to Odd-Numbered Exercises<\/h2>\n<p>1.\u00a0The terms of a polynomial do not have to have a common factor for the entire polynomial to be factorable. For example, [latex]4{x}^{2}[\/latex] and [latex]-9{y}^{2}[\/latex] don\u2019t have a common factor, but the whole polynomial is still factorable: [latex]4{x}^{2}-9{y}^{2}=\\left(2x+3y\\right)\\left(2x - 3y\\right)[\/latex].<\/p>\n<p>3.\u00a0Divide the [latex]x[\/latex] term into the sum of two terms, factor each portion of the expression separately, and then factor out the GCF of the entire expression.<\/p>\n<p>5.\u00a0[latex]7m[\/latex]<\/p>\n<p>7.\u00a0[latex]10{m}^{3}[\/latex]<\/p>\n<p>9.\u00a0[latex]y[\/latex]<\/p>\n<p>11.\u00a0[latex]\\left(2a - 3\\right)\\left(a+6\\right)[\/latex]<\/p>\n<p>13.\u00a0[latex]\\left(3n - 11\\right)\\left(2n+1\\right)[\/latex]<\/p>\n<p>15.\u00a0[latex]\\left(p+1\\right)\\left(2p - 7\\right)[\/latex]<\/p>\n<p>17.\u00a0[latex]\\left(5h+3\\right)\\left(2h - 3\\right)[\/latex]<\/p>\n<p>19.\u00a0[latex]\\left(9d - 1\\right)\\left(d - 8\\right)[\/latex]<\/p>\n<p>21.\u00a0[latex]\\left(12t+13\\right)\\left(t - 1\\right)[\/latex]<\/p>\n<p>23.\u00a0[latex]\\left(4x+10\\right)\\left(4x - 10\\right)[\/latex]<\/p>\n<p>25.\u00a0[latex]\\left(11p+13\\right)\\left(11p - 13\\right)[\/latex]<\/p>\n<p>27.\u00a0[latex]\\left(19d+9\\right)\\left(19d - 9\\right)[\/latex]<\/p>\n<p>29.\u00a0[latex]\\left(12b+5c\\right)\\left(12b - 5c\\right)[\/latex]<\/p>\n<p>31.\u00a0[latex]{\\left(7n+12\\right)}^{2}[\/latex]<\/p>\n<p>33.\u00a0[latex]{\\left(15y+4\\right)}^{2}[\/latex]<\/p>\n<p>35.\u00a0[latex]{\\left(5p - 12\\right)}^{2}[\/latex]<\/p>\n<p>37.\u00a0[latex]\\left(x+6\\right)\\left({x}^{2}-6x+36\\right)[\/latex]<\/p>\n<p>39.\u00a0[latex]\\left(5a+7\\right)\\left(25{a}^{2}-35a+49\\right)[\/latex]<\/p>\n<p>41.\u00a0[latex]\\left(4x - 5\\right)\\left(16{x}^{2}+20x+25\\right)[\/latex]<\/p>\n<p>43.\u00a0[latex]\\left(5r+12s\\right)\\left(25{r}^{2}-60rs+144{s}^{2}\\right)[\/latex]<\/p>\n<p>45.\u00a0[latex]{\\left(2c+3\\right)}^{-\\frac{1}{4}}\\left(-7c - 15\\right)[\/latex]<\/p>\n<p>47.\u00a0[latex]{\\left(x+2\\right)}^{-\\frac{2}{5}}\\left(19x+10\\right)[\/latex]<\/p>\n<p>49.\u00a0[latex]{\\left(2z - 9\\right)}^{-\\frac{3}{2}}\\left(27z - 99\\right)[\/latex]<\/p>\n<p>51.\u00a0[latex]\\left(14x - 3\\right)\\left(7x+9\\right)[\/latex]<\/p>\n<p>53.\u00a0[latex]\\left(3x+5\\right)\\left(3x - 5\\right)[\/latex]<\/p>\n<p>55.\u00a0[latex]{\\left(2x+5\\right)}^{2}{\\left(2x - 5\\right)}^{2}[\/latex]<\/p>\n<p>57.\u00a0[latex]\\left(4{z}^{2}+49{a}^{2}\\right)\\left(2z+7a\\right)\\left(2z - 7a\\right)[\/latex]<\/p>\n<p>59.\u00a0[latex]\\frac{1}{\\left(4x+9\\right)\\left(4x - 9\\right)\\left(2x+3\\right)}[\/latex]<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-319\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: OpenStax College Algebra. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":276,"menu_order":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"College Algebra\",\"author\":\"OpenStax College Algebra\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-319","chapter","type-chapter","status-publish","hentry"],"part":205,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/319","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/319\/revisions"}],"predecessor-version":[{"id":588,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/319\/revisions\/588"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/205"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/319\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/media?parent=319"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=319"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/contributor?post=319"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/license?post=319"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}