{"id":271799,"date":"2025-07-26T07:10:08","date_gmt":"2025-07-26T07:10:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=271799"},"modified":"2025-07-26T07:10:10","modified_gmt":"2025-07-26T07:10:10","slug":"in-order-to-factor-x-2-2x-8-we-must-break-up-the-bx-term-into-two-terms-whose-coefficients-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/26\/in-order-to-factor-x-2-2x-8-we-must-break-up-the-bx-term-into-two-terms-whose-coefficients-2\/","title":{"rendered":"In order to factor x ^ 2 &#8211; 2x &#8211; 8 we must break up the &#8220;bx&#8221; term into two terms whose coefficients\u2026"},"content":{"rendered":"\n<p>In order to factor x ^ 2 &#8211; 2x &#8211; 8 we must break up the &#8220;bx&#8221; term into two terms whose coefficients\u2026<br>add to-2 and multiply to -8.<br>add to &amp; and multiply to 2.<br>add to 1 and multiply to -8.<br>odd to 1 and multiply to 2<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To factor the quadratic expression x2\u22122x\u22128x^2 &#8211; 2x &#8211; 8, we need to break up the middle term \u22122x-2x into two terms whose coefficients both add up to -2 and multiply to give the product of the constant term (-8).<\/p>\n\n\n\n<p>Let\u2019s start by identifying the factors of -8 that sum up to -2. The pairs of numbers that multiply to -8 are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1 and -8<\/li>\n\n\n\n<li>-1 and 8<\/li>\n\n\n\n<li>2 and -4<\/li>\n\n\n\n<li>-2 and 4<\/li>\n<\/ul>\n\n\n\n<p>Now, let\u2019s check the sums of these pairs:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1+(\u22128)=\u221271 + (-8) = -7<\/li>\n\n\n\n<li>\u22121+8=7-1 + 8 = 7<\/li>\n\n\n\n<li>2+(\u22124)=\u221222 + (-4) = -2 (This is the pair we want!)<\/li>\n\n\n\n<li>\u22122+4=2-2 + 4 = 2<\/li>\n<\/ul>\n\n\n\n<p>The pair that adds up to -2 is 22 and \u22124-4, so we will break up the middle term \u22122x-2x into 2x2x and \u22124x-4x. The expression then becomes: x2+2x\u22124x\u22128x^2 + 2x &#8211; 4x &#8211; 8<\/p>\n\n\n\n<p>Now, group the terms in pairs: (x2+2x)\u2212(4x+8)(x^2 + 2x) &#8211; (4x + 8)<\/p>\n\n\n\n<p>Factor out the greatest common factor (GCF) from each group: x(x+2)\u22124(x+2)x(x + 2) &#8211; 4(x + 2)<\/p>\n\n\n\n<p>Notice that both terms contain (x+2)(x + 2), so factor this common binomial out: (x\u22124)(x+2)(x &#8211; 4)(x + 2)<\/p>\n\n\n\n<p>Thus, the factored form of x2\u22122x\u22128x^2 &#8211; 2x &#8211; 8 is (x\u22124)(x+2)(x &#8211; 4)(x + 2).<\/p>\n\n\n\n<p>In summary, by identifying the correct pair of numbers that multiply to -8 and add to -2, we can break up the middle term and factor the quadratic expression into two binomials. This technique is known as factoring by grouping.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In order to factor x ^ 2 &#8211; 2x &#8211; 8 we must break up the &#8220;bx&#8221; term into two terms whose coefficients\u2026add to-2 and multiply to -8.add to &amp; and multiply to 2.add to 1 and multiply to -8.odd to 1 and multiply to 2 The correct answer and explanation is: To factor the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-271799","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271799","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=271799"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271799\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271799"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271799"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271799"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}