{"id":271760,"date":"2025-07-26T06:44:50","date_gmt":"2025-07-26T06:44:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=271760"},"modified":"2025-07-26T06:44:52","modified_gmt":"2025-07-26T06:44:52","slug":"in-order-to-factor-x-2-2x-8-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-8-we-must-break-up-the-bx-term-into-two-terms-whose-coefficients\/","title":{"rendered":"In order to factor x ^ 2 – 2x – 8 we must break up the “bx” term into two terms whose coefficients"},"content":{"rendered":"\n

In order to factor x ^ 2 – 2x – 8 we must break up the “bx” term into two terms whose coefficients\u2026
add to-2 and multiply to 8.
add to 8 and multiply to 2.
add to 1 and multiply to -8.
add to 1 and multiply to 2.<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is add to -2 and multiply to -8<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

When factoring a quadratic expression of the form ax^2 + bx + c<\/strong>, the goal is to find two numbers that multiply to ac<\/strong> and add to b<\/strong>. In this case, the quadratic expression is x^2 – 2x – 8<\/strong>. Here, a = 1<\/strong>, b = -2<\/strong>, and c = -8<\/strong>.<\/p>\n\n\n\n

To factor this quadratic, we need to find two numbers that:<\/p>\n\n\n\n

    \n
  1. Multiply to a * c = 1 * (-8) = -8<\/strong>.<\/li>\n\n\n\n
  2. Add up to b = -2<\/strong>.<\/li>\n<\/ol>\n\n\n\n

    Now, let’s find two numbers that meet these conditions:<\/p>\n\n\n\n

      \n
    • The factors of -8<\/strong> are:\n
        \n
      • (1, -8)<\/li>\n\n\n\n
      • (-1, 8)<\/li>\n\n\n\n
      • (2, -4)<\/li>\n\n\n\n
      • (-2, 4)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

        Out of these pairs, -4<\/strong> and 2<\/strong> add up to -2<\/strong>. Therefore, these are the numbers that we need to break up the bx<\/strong> term.<\/p>\n\n\n\n

        Step-by-step process:<\/h3>\n\n\n\n
          \n
        1. Start with the original quadratic: x^2 – 2x – 8<\/strong>.<\/li>\n\n\n\n
        2. Break up the bx<\/strong> term -2x<\/strong> into -4x + 2x<\/strong>: x2\u22124x+2x\u22128x^2 – 4x + 2x – 8<\/li>\n\n\n\n
        3. Factor by grouping:
          • Group the first two terms: x^2 – 4x<\/strong>.<\/li>
          • Group the last two terms: 2x – 8<\/strong>.<\/li><\/ul>(x2\u22124x)+(2x\u22128)(x^2 – 4x) + (2x – 8)<\/li>\n\n\n\n
          • Factor out the greatest common factor (GCF) from each group:
            • From x^2 – 4x<\/strong>, factor out x<\/strong>: x(x – 4)<\/strong>.<\/li>
            • From 2x – 8<\/strong>, factor out 2<\/strong>: 2(x – 4)<\/strong>.<\/li><\/ul>x(x\u22124)+2(x\u22124)x(x – 4) + 2(x – 4)<\/li>\n\n\n\n
            • Now, factor out the common binomial factor (x – 4)<\/strong>: (x\u22124)(x+2)(x – 4)(x + 2)<\/li>\n<\/ol>\n\n\n\n

              Thus, the factored form of x^2 – 2x – 8<\/strong> is (x – 4)(x + 2)<\/strong>.<\/p>\n\n\n\n

              This demonstrates the factoring process and shows that the correct numbers to split the bx<\/strong> term were -4<\/strong> and 2<\/strong>, which add up to -2<\/strong> and multiply to -8<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

              In order to factor x ^ 2 – 2x – 8 we must break up the “bx” term into two terms whose coefficients\u2026add to-2 and multiply to 8.add to 8 and multiply to 2.add to 1 and multiply to -8.add to 1 and multiply to 2. The correct answer and explanation is: The correct answer […]<\/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-271760","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271760","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=271760"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271760\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271760"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271760"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271760"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}