{"id":232162,"date":"2025-06-11T18:49:14","date_gmt":"2025-06-11T18:49:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=232162"},"modified":"2025-06-11T18:49:16","modified_gmt":"2025-06-11T18:49:16","slug":"choose-any-block-and-factorise","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/11\/choose-any-block-and-factorise\/","title":{"rendered":"CHOOSE ANY BLOCK AND FACTORISE"},"content":{"rendered":"\n


CHOOSE ANY BLOCK AND FACTORISE 2x\u00b2 + 7x +3 2x\u00b2 – 12x + 10 1) 2x\u00b2 + 5x + 2 3x\u00b2 + 23x + 14 3x\u00b2 – 7x + 2 2) 2x\u00b2 + 11x + 12 2x\u00b2 + 14x + 20 3x\u00b2 + 8x – 3 3) 6x\u00b2 + 7x + 2 5x\u00b2 + 29x + 36 3x\u00b2 – 5x – 2 4) 3x\u00b2 – 7x + 2<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Of the blocks provided, the third block is selected for factorization. This block contains four quadratic trinomials of the form ax\u00b2 + bx + c.<\/p>\n\n\n\n

Introduction to Factorising Quadratic Trinomials<\/strong><\/p>\n\n\n\n

Factorising a quadratic trinomial is the process of expressing it as a product of two linear binomials. The most common method for trinomials where the leading coefficient ‘a’ is not 1 is the ‘ac method’, also known as factoring by grouping or splitting the middle term.<\/p>\n\n\n\n

The procedure involves these steps:<\/p>\n\n\n\n

    \n
  1. Identify the coefficients a, b, and c in the expression ax\u00b2 + bx + c.<\/li>\n\n\n\n
  2. Calculate the product of a and c (ac).<\/li>\n\n\n\n
  3. Find two numbers that multiply to give the value ‘ac’ and add to give the value ‘b’.<\/li>\n\n\n\n
  4. Rewrite the middle term ‘bx’ as the sum of two terms using the numbers found in the previous step.<\/li>\n\n\n\n
  5. Factor the resulting four-term polynomial by grouping the terms into two pairs and extracting the common factors.<\/li>\n<\/ol>\n\n\n\n

    Solutions for Block 3<\/strong><\/p>\n\n\n\n

    1) Factorise 2x\u00b2 + 5x + 2<\/strong><\/p>\n\n\n\n

      \n
    • Here, a = 2, b = 5, and c = 2.<\/li>\n\n\n\n
    • The product ac = 2 \u00d7 2 = 4.<\/li>\n\n\n\n
    • Two numbers that multiply to 4 and add to 5 are 4 and 1.<\/li>\n\n\n\n
    • Rewrite the expression: 2x\u00b2 + 4x + 1x + 2<\/li>\n\n\n\n
    • Factor by grouping: (2x\u00b2 + 4x) + (x + 2) = 2x(x + 2) + 1(x + 2)<\/li>\n\n\n\n
    • The factored form is\u00a0(2x + 1)(x + 2)<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      2) Factorise 2x\u00b2 + 11x + 12<\/strong><\/p>\n\n\n\n

        \n
      • Here, a = 2, b = 11, and c = 12.<\/li>\n\n\n\n
      • The product ac = 2 \u00d7 12 = 24.<\/li>\n\n\n\n
      • Two numbers that multiply to 24 and add to 11 are 8 and 3.<\/li>\n\n\n\n
      • Rewrite the expression: 2x\u00b2 + 8x + 3x + 12<\/li>\n\n\n\n
      • Factor by grouping: (2x\u00b2 + 8x) + (3x + 12) = 2x(x + 4) + 3(x + 4)<\/li>\n\n\n\n
      • The factored form is\u00a0(2x + 3)(x + 4)<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        3) Factorise 6x\u00b2 + 7x + 2<\/strong><\/p>\n\n\n\n

          \n
        • Here, a = 6, b = 7, and c = 2.<\/li>\n\n\n\n
        • The product ac = 6 \u00d7 2 = 12.<\/li>\n\n\n\n
        • Two numbers that multiply to 12 and add to 7 are 4 and 3.<\/li>\n\n\n\n
        • Rewrite the expression: 6x\u00b2 + 4x + 3x + 2<\/li>\n\n\n\n
        • Factor by grouping: (6x\u00b2 + 4x) + (3x + 2) = 2x(3x + 2) + 1(3x + 2)<\/li>\n\n\n\n
        • The factored form is\u00a0(2x + 1)(3x + 2)<\/strong>.<\/li>\n<\/ul>\n\n\n\n

          4) Factorise 3x\u00b2 – 7x + 2<\/strong><\/p>\n\n\n\n

            \n
          • Here, a = 3, b = -7, and c = 2.<\/li>\n\n\n\n
          • The product ac = 3 \u00d7 2 = 6.<\/li>\n\n\n\n
          • Two numbers that multiply to 6 and add to -7 are -6 and -1.<\/li>\n\n\n\n
          • Rewrite the expression: 3x\u00b2 – 6x – 1x + 2<\/li>\n\n\n\n
          • Factor by grouping: (3x\u00b2 – 6x) – (x – 2) = 3x(x – 2) – 1(x – 2)<\/li>\n\n\n\n
          • The factored form is\u00a0(3x – 1)(x – 2)<\/strong>.<\/li>\n<\/ul>\n\n\n\n
            \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

            CHOOSE ANY BLOCK AND FACTORISE 2x\u00b2 + 7x +3 2x\u00b2 – 12x + 10 1) 2x\u00b2 + 5x + 2 3x\u00b2 + 23x + 14 3x\u00b2 – 7x + 2 2) 2x\u00b2 + 11x + 12 2x\u00b2 + 14x + 20 3x\u00b2 + 8x – 3 3) 6x\u00b2 + 7x + 2 5x\u00b2 + 29x […]<\/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-232162","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232162","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=232162"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/232162\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=232162"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=232162"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=232162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}