{"id":271789,"date":"2025-07-26T07:00:08","date_gmt":"2025-07-26T07:00:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=271789"},"modified":"2025-07-26T07:00:11","modified_gmt":"2025-07-26T07:00:11","slug":"in-order-to-factor-x-2-2x-24-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-24-we-must-break-up-the-bx-term-into-two-terms-whose-coefficients-2\/","title":{"rendered":"In order to factor x ^ 2 – 2x – 24 we must break up the “bx” term into two terms whose coefficients"},"content":{"rendered":"\n

In order to factor x ^ 2 – 2x – 24 we must break up the “bx” term into two terms whose coefficients\u2026
add 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.<\/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 -24”<\/strong>.<\/p>\n\n\n\n

To factor the quadratic expression x2\u22122x\u221224x^2 – 2x – 24, we start by looking at the form of a general quadratic equation, which is ax2+bx+cax^2 + bx + c. Here, a=1a = 1, b=\u22122b = -2, and c=\u221224c = -24.<\/p>\n\n\n\n

Step 1: Identify the numbers<\/h3>\n\n\n\n

We need two numbers that:<\/p>\n\n\n\n

    \n
  1. Add up to the coefficient of the middle term, which is b=\u22122b = -2.<\/li>\n\n\n\n
  2. Multiply to the product of the coefficient of x2x^2 (which is 1) and the constant term c=\u221224c = -24. In this case, we need two numbers that multiply to 1\u00d7(\u221224)=\u2212241 \\times (-24) = -24.<\/li>\n<\/ol>\n\n\n\n

    Step 2: List possible pairs<\/h3>\n\n\n\n

    Now, we look for pairs of numbers that multiply to -24 and check if their sum equals -2. The pairs of factors of -24 are:<\/p>\n\n\n\n

      \n
    • 1\u00d7(\u221224)=\u2212241 \\times (-24) = -24<\/li>\n\n\n\n
    • 2\u00d7(\u221212)=\u2212242 \\times (-12) = -24<\/li>\n\n\n\n
    • 3\u00d7(\u22128)=\u2212243 \\times (-8) = -24<\/li>\n\n\n\n
    • 4\u00d7(\u22126)=\u2212244 \\times (-6) = -24<\/li>\n\n\n\n
    • \u22121\u00d724=\u221224-1 \\times 24 = -24<\/li>\n\n\n\n
    • \u22122\u00d712=\u221224-2 \\times 12 = -24<\/li>\n\n\n\n
    • \u22123\u00d78=\u221224-3 \\times 8 = -24<\/li>\n\n\n\n
    • \u22124\u00d76=\u221224-4 \\times 6 = -24<\/li>\n<\/ul>\n\n\n\n

      The pair that adds up to -2 is \u22126-6 and 44, because: \u22126+4=\u22122-6 + 4 = -2<\/p>\n\n\n\n

      Step 3: Rewrite the middle term<\/h3>\n\n\n\n

      Now, we can break up the middle term \u22122x-2x into two terms using \u22126x-6x and 4x4x: x2\u22126x+4x\u221224x^2 – 6x + 4x – 24<\/p>\n\n\n\n

      Step 4: Factor by grouping<\/h3>\n\n\n\n

      Next, we factor by grouping. We group the first two terms and the last two terms: (x2\u22126x)+(4x\u221224)(x^2 – 6x) + (4x – 24)<\/p>\n\n\n\n

      Now, factor out the greatest common factor (GCF) from each group: x(x\u22126)+4(x\u22126)x(x – 6) + 4(x – 6)<\/p>\n\n\n\n

      Step 5: Final factorization<\/h3>\n\n\n\n

      Finally, factor out the common binomial factor (x\u22126)(x – 6): (x+4)(x\u22126)(x + 4)(x – 6)<\/p>\n\n\n\n

      So, the factored form of x2\u22122x\u221224x^2 – 2x – 24 is (x+4)(x\u22126)(x + 4)(x – 6).<\/p>\n\n\n\n

      Thus, the correct pair of numbers is the one that adds to -2 and multiplies to -24.<\/p>\n","protected":false},"excerpt":{"rendered":"

      In order to factor x ^ 2 – 2x – 24 we must break up the “bx” 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 […]<\/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-271789","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271789","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=271789"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271789\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271789"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271789"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}