{"id":17876,"date":"2020-04-11T23:35:00","date_gmt":"2020-04-11T23:35:00","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/?post_type=chapter&#038;p=17876"},"modified":"2024-04-30T23:20:40","modified_gmt":"2024-04-30T23:20:40","slug":"summary-factoring-trinomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/summary-factoring-trinomials\/","title":{"raw":"Summary: Factoring Methods","rendered":"Summary: Factoring Methods"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<h3>Factoring Trinomials in the form [latex]ax^{2}+bx+c[\/latex]<\/h3>\r\n<p style=\"padding-left: 60px;\">To factor a trinomial in the form [latex]ax^{2}+bx+c[\/latex], find two integers, <i>r<\/i> and <i>s<\/i>, whose sum is <i>b<\/i> and whose product is <i>ac.<\/i><\/p>\r\n<p style=\"text-align: center; padding-left: 60px;\">[latex]\\begin{array}{l}r\\cdot{s}=a\\cdot{c}\\\\r+s=b\\end{array}[\/latex]<\/p>\r\n<p style=\"padding-left: 60px;\">Rewrite the trinomial as [latex]ax^{2}+rx+sx+c[\/latex] and then use grouping and the distributive property to factor the polynomial.<\/p>\r\n\r\n<h3>How to factor a trinomial in the form [latex]a{x}^{2}+bx+c[\/latex] by grouping<\/h3>\r\n<ol>\r\n \t<li>List factors of [latex]ac[\/latex].<\/li>\r\n \t<li>Find [latex]p[\/latex] and [latex]q[\/latex], a pair of factors of [latex]ac[\/latex] with a sum of [latex]b[\/latex].<\/li>\r\n \t<li>Rewrite the original expression as [latex]a{x}^{2}+px+qx+c[\/latex].<\/li>\r\n \t<li>Pull out the GCF of [latex]a{x}^{2}+px[\/latex].<\/li>\r\n \t<li>Pull out the GCF of [latex]qx+c[\/latex].<\/li>\r\n \t<li>Factor out the GCF of the expression.<\/li>\r\n<\/ol>\r\n<h3>Factoring Trinomials in the form\u00a0[latex]x^{2}+bx+c[\/latex]<\/h3>\r\n<p style=\"padding-left: 60px;\">To factor a trinomial in the form [latex]x^{2}+bx+c[\/latex], find two integers, <i>r<\/i> and <i>s<\/i>, whose product is <i>c <\/i>and whose sum is <i>b<\/i>.<\/p>\r\n<p style=\"text-align: center; padding-left: 60px;\">[latex]\\begin{array}{l}r\\cdot{s}=c\\\\\\text{ and }\\\\r+s=b\\end{array}[\/latex]<\/p>\r\n<p style=\"padding-left: 60px;\">Rewrite the trinomial as [latex]x^{2}+rx+sx+c[\/latex]\u00a0and then use grouping and the distributive property to factor the polynomial. The resulting factors will be [latex]\\left(x+r\\right)[\/latex] and [latex]\\left(x+s\\right)[\/latex].<\/p>\r\n\r\n<h3>How to factor a trinomial in the form [latex]{x}^{2}+bx+c[\/latex]<\/h3>\r\n<ol>\r\n \t<li>List factors of [latex]c[\/latex].<\/li>\r\n \t<li>Find [latex]p[\/latex] and [latex]q[\/latex], a pair of factors of [latex]c[\/latex] with a sum of [latex]b[\/latex].<\/li>\r\n \t<li>Write the factored expression [latex]\\left(x+p\\right)\\left(x+q\\right)[\/latex].<\/li>\r\n<\/ol>\r\n<h2>Glossary<\/h2>\r\n<strong>Prime trinomial<\/strong> - A trinomial that cannot be factored using integers\r\n","rendered":"<h2>Key Concepts<\/h2>\n<h3>Factoring Trinomials in the form [latex]ax^{2}+bx+c[\/latex]<\/h3>\n<p style=\"padding-left: 60px;\">To factor a trinomial in the form [latex]ax^{2}+bx+c[\/latex], find two integers, <i>r<\/i> and <i>s<\/i>, whose sum is <i>b<\/i> and whose product is <i>ac.<\/i><\/p>\n<p style=\"text-align: center; padding-left: 60px;\">[latex]\\begin{array}{l}r\\cdot{s}=a\\cdot{c}\\\\r+s=b\\end{array}[\/latex]<\/p>\n<p style=\"padding-left: 60px;\">Rewrite the trinomial as [latex]ax^{2}+rx+sx+c[\/latex] and then use grouping and the distributive property to factor the polynomial.<\/p>\n<h3>How to factor a trinomial in the form [latex]a{x}^{2}+bx+c[\/latex] by grouping<\/h3>\n<ol>\n<li>List factors of [latex]ac[\/latex].<\/li>\n<li>Find [latex]p[\/latex] and [latex]q[\/latex], a pair of factors of [latex]ac[\/latex] with a sum of [latex]b[\/latex].<\/li>\n<li>Rewrite the original expression as [latex]a{x}^{2}+px+qx+c[\/latex].<\/li>\n<li>Pull out the GCF of [latex]a{x}^{2}+px[\/latex].<\/li>\n<li>Pull out the GCF of [latex]qx+c[\/latex].<\/li>\n<li>Factor out the GCF of the expression.<\/li>\n<\/ol>\n<h3>Factoring Trinomials in the form\u00a0[latex]x^{2}+bx+c[\/latex]<\/h3>\n<p style=\"padding-left: 60px;\">To factor a trinomial in the form [latex]x^{2}+bx+c[\/latex], find two integers, <i>r<\/i> and <i>s<\/i>, whose product is <i>c <\/i>and whose sum is <i>b<\/i>.<\/p>\n<p style=\"text-align: center; padding-left: 60px;\">[latex]\\begin{array}{l}r\\cdot{s}=c\\\\\\text{ and }\\\\r+s=b\\end{array}[\/latex]<\/p>\n<p style=\"padding-left: 60px;\">Rewrite the trinomial as [latex]x^{2}+rx+sx+c[\/latex]\u00a0and then use grouping and the distributive property to factor the polynomial. The resulting factors will be [latex]\\left(x+r\\right)[\/latex] and [latex]\\left(x+s\\right)[\/latex].<\/p>\n<h3>How to factor a trinomial in the form [latex]{x}^{2}+bx+c[\/latex]<\/h3>\n<ol>\n<li>List factors of [latex]c[\/latex].<\/li>\n<li>Find [latex]p[\/latex] and [latex]q[\/latex], a pair of factors of [latex]c[\/latex] with a sum of [latex]b[\/latex].<\/li>\n<li>Write the factored expression [latex]\\left(x+p\\right)\\left(x+q\\right)[\/latex].<\/li>\n<\/ol>\n<h2>Glossary<\/h2>\n<p><strong>Prime trinomial<\/strong> &#8211; A trinomial that cannot be factored using integers<\/p>\n","protected":false},"author":253111,"menu_order":12,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"8076008d880d480494979e137e1b2ada","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-17876","chapter","type-chapter","status-publish","hentry"],"part":16188,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17876","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/users\/253111"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17876\/revisions"}],"predecessor-version":[{"id":20490,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17876\/revisions\/20490"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/16188"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17876\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/media?parent=17876"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=17876"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=17876"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/license?post=17876"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}