{"id":271739,"date":"2025-07-26T06:33:32","date_gmt":"2025-07-26T06:33:32","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=271739"},"modified":"2025-07-26T06:33:34","modified_gmt":"2025-07-26T06:33:34","slug":"in-order-to-factor-x-2-2x-24-we-must-break-up-the-bx-term-into-two-terms-whose-coefficients","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/26\/in-order-to-factor-x-2-2x-24-we-must-break-up-the-bx-term-into-two-terms-whose-coefficients\/","title":{"rendered":"In order to factor x ^ 2 &#8211; 2x &#8211; 24 we must break up the &#8220;bx&#8221; term into two terms whose coefficients"},"content":{"rendered":"\n<p>In order to factor x ^ 2 &#8211; 2x &#8211; 24 we must break up the &#8220;bx&#8221; term into two terms whose coefficients\u2026<br>add to-1 and multiply to -2.<br>add to 1 and multiply to -24.<br>add to-24 and multiply to -2.<br>add to -2 and multiply to -24.<\/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>The correct answer is: <strong>add to -2 and multiply to -24.<\/strong><\/p>\n\n\n\n<p>Here&#8217;s the explanation:<\/p>\n\n\n\n<p>When factoring a quadratic expression in the form of x2+bx+cx^2 + bx + c, the goal is to find two numbers that add to the coefficient of the xx-term (which is bb) and multiply to the constant term (which is cc).<\/p>\n\n\n\n<p>For the given quadratic expression x2\u22122x\u221224x^2 &#8211; 2x &#8211; 24, we need to break the middle term \u22122x-2x into two terms whose coefficients:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Add to \u22122-2 (the coefficient of xx),<\/li>\n\n\n\n<li>Multiply to \u221224-24 (the constant term).<\/li>\n<\/ul>\n\n\n\n<p>We are looking for two numbers, say mm and nn, that satisfy these two conditions:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>m+n=\u22122m + n = -2 (the sum of the numbers must be equal to \u22122-2),<\/li>\n\n\n\n<li>m\u00d7n=\u221224m \\times n = -24 (the product of the numbers must be equal to \u221224-24).<\/li>\n<\/ol>\n\n\n\n<p>By examining possible factor pairs of \u221224-24, we get:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1\u00d7\u2212241 \\times -24,<\/li>\n\n\n\n<li>\u22121\u00d724-1 \\times 24,<\/li>\n\n\n\n<li>2\u00d7\u2212122 \\times -12,<\/li>\n\n\n\n<li>\u22122\u00d712-2 \\times 12,<\/li>\n\n\n\n<li>3\u00d7\u221283 \\times -8,<\/li>\n\n\n\n<li>\u22123\u00d78-3 \\times 8,<\/li>\n\n\n\n<li>4\u00d7\u221264 \\times -6,<\/li>\n\n\n\n<li>\u22124\u00d76-4 \\times 6.<\/li>\n<\/ul>\n\n\n\n<p>Out of these, the pair that adds up to \u22122-2 is 44 and \u22126-6. That is:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>4+(\u22126)=\u221224 + (-6) = -2,<\/li>\n\n\n\n<li>4\u00d7(\u22126)=\u2212244 \\times (-6) = -24.<\/li>\n<\/ul>\n\n\n\n<p>So, we can rewrite \u22122x-2x as 4x\u22126x4x &#8211; 6x, which gives the expression: x2+4x\u22126x\u221224.x^2 + 4x &#8211; 6x &#8211; 24.<\/p>\n\n\n\n<p>Next, we factor by grouping: x(x+4)\u22126(x+4).x(x + 4) &#8211; 6(x + 4).<\/p>\n\n\n\n<p>Now, we factor out the common binomial (x+4)(x + 4): (x\u22126)(x+4).(x &#8211; 6)(x + 4).<\/p>\n\n\n\n<p>Thus, the factored form of x2\u22122x\u221224x^2 &#8211; 2x &#8211; 24 is (x\u22126)(x+4)(x &#8211; 6)(x + 4).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In order to factor x ^ 2 &#8211; 2x &#8211; 24 we must break up the &#8220;bx&#8221; term into two terms whose coefficients\u2026add to-1 and multiply to -2.add to 1 and multiply to -24.add to-24 and multiply to -2.add to -2 and multiply to -24. The correct answer and explanation is: The correct answer is: [&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-271739","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271739","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=271739"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271739\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271739"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271739"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271739"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}