{"id":271797,"date":"2025-07-26T07:04:02","date_gmt":"2025-07-26T07:04:02","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=271797"},"modified":"2025-07-26T07:04:06","modified_gmt":"2025-07-26T07:04:06","slug":"in-order-to-factor-x-2-5x-6-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-2-5x-6-we-must-break-up-the-bx-term-into-two-terms-whose-coefficients\/","title":{"rendered":"In order to factor x ^ 2 + 5x + 6 we must break up the “bx” term into two terms whose coefficients"},"content":{"rendered":"\n

In order to factor x ^ 2 + 5x + 6 we must break up the “bx” term into two terms whose coefficients\u2026
add to 5 and multiply to 6
add to 6 and multiply to 5.
add to 1 and multiply to f.
add to 1 and multiply to 5.<\/p>\n\n\n\n

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

The correct answer is: add to 5 and multiply to 6.<\/strong><\/p>\n\n\n\n

To factor the quadratic expression x2+5x+6x^2 + 5x + 6, we start by looking for two numbers that multiply to give the constant term (6) and add up to give the coefficient of the linear term (5).<\/p>\n\n\n\n

    \n
  1. The quadratic is in the standard form ax2+bx+cax^2 + bx + c, where:\n
      \n
    • a=1a = 1 (the coefficient of x2x^2),<\/li>\n\n\n\n
    • b=5b = 5 (the coefficient of xx),<\/li>\n\n\n\n
    • c=6c = 6 (the constant term).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • We need two numbers that meet the following criteria:\n
        \n
      • Their product is c=6c = 6,<\/li>\n\n\n\n
      • Their sum is b=5b = 5.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • The possible pairs of numbers that multiply to 6 are:\n
          \n
        • 1 and 6 (since 1\u00d76=61 \\times 6 = 6),<\/li>\n\n\n\n
        • 2 and 3 (since 2\u00d73=62 \\times 3 = 6).<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • Now, check which pair adds up to 5:\n
            \n
          • 1+6=71 + 6 = 7 (not 5),<\/li>\n\n\n\n
          • 2+3=52 + 3 = 5 (this works).<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

            So, the correct pair is 22 and 33. These numbers both multiply to 6 and add up to 5.<\/p>\n\n\n\n

              \n
            1. Now, break up the middle term 5x5x into 2x+3x2x + 3x and rewrite the quadratic as: x2+2x+3x+6.x^2 + 2x + 3x + 6.<\/li>\n\n\n\n
            2. Factor by grouping:
              • Group the first two terms: x2+2xx^2 + 2x,<\/li>
              • Group the last two terms: 3x+63x + 6.<\/li><\/ul>Factor each group: x(x+2)+3(x+2).x(x + 2) + 3(x + 2).<\/li>\n\n\n\n
              • Finally, factor out the common binomial factor (x+2)(x + 2): (x+2)(x+3).(x + 2)(x + 3).<\/li>\n<\/ol>\n\n\n\n

                Thus, the factorization of x2+5x+6x^2 + 5x + 6 is (x+2)(x+3)(x + 2)(x + 3).<\/p>\n","protected":false},"excerpt":{"rendered":"

                In order to factor x ^ 2 + 5x + 6 we must break up the “bx” term into two terms whose coefficients\u2026add to 5 and multiply to 6add to 6 and multiply to 5.add to 1 and multiply to f.add to 1 and multiply to 5. The correct answer and explanation is: The correct […]<\/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-271797","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271797","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=271797"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271797\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271797"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271797"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271797"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}