{"id":266812,"date":"2025-07-23T07:26:24","date_gmt":"2025-07-23T07:26:24","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=266812"},"modified":"2025-07-23T07:26:27","modified_gmt":"2025-07-23T07:26:27","slug":"factor-the-perfect-square-trinomial","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/23\/factor-the-perfect-square-trinomial\/","title":{"rendered":"Factor the perfect square trinomial"},"content":{"rendered":"\n

point) Factor the perfect square trinomial x2 8x + 16.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

The correct factored form of the perfect square trinomial x\u00b2 – 8x + 16 is (x – 4)\u00b2<\/strong>.<\/p>\n\n\n\n

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

A perfect square trinomial is a specific type of quadratic expression that is the result of squaring a binomial. There are two standard patterns to recognize for perfect square trinomials:<\/p>\n\n\n\n

    \n
  1. a\u00b2 + 2ab + b\u00b2 = (a + b)\u00b2<\/li>\n\n\n\n
  2. a\u00b2 – 2ab + b\u00b2 = (a – b)\u00b2<\/li>\n<\/ol>\n\n\n\n

    To factor the given expression, x\u00b2 – 8x + 16, we need to determine if it fits one of these patterns.<\/p>\n\n\n\n

    Step 1: Identify the ‘a’ and ‘b’ terms.<\/strong>
    First, we look at the first and last terms of the trinomial to see if they are perfect squares.
    The first term is x\u00b2. This is the square of x. So, we can set a = x<\/strong>.
    The last term is 16. This is the square of 4. So, we can set b = 4<\/strong>.<\/p>\n\n\n\n

    Step 2: Check the middle term.<\/strong>
    Now, we must verify if the middle term, -8x, matches the pattern. Since the middle term is negative, we should check it against the second formula’s middle term, which is -2ab.<\/p>\n\n\n\n

    Let\u2019s substitute our values of ‘a’ and ‘b’ into this formula:
    -2ab = -2 * (x) * (4) = -8x<\/p>\n\n\n\n

    The result, -8x, is exactly the same as the middle term in our original expression. This confirms that the trinomial x\u00b2 – 8x + 16 is a perfect square and fits the pattern a\u00b2 – 2ab + b\u00b2.<\/p>\n\n\n\n

    Step 3: Write the factored form.<\/strong>
    Since the trinomial matches the pattern a\u00b2 – 2ab + b\u00b2, its factored form is (a – b)\u00b2. We can now substitute our values for ‘a’ and ‘b’ into this factored form:
    (a – b)\u00b2 = (x – 4)\u00b2<\/p>\n\n\n\n

    To double check the answer, you can expand (x – 4)\u00b2:
    (x – 4)(x – 4) = x\u00b2 – 4x – 4x + 16 = x\u00b2 – 8x + 16.
    This matches the original expression, confirming our factorization is correct.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    point) Factor the perfect square trinomial x2 8x + 16. The Correct Answer and Explanation is: The correct factored form of the perfect square trinomial x\u00b2 – 8x + 16 is (x – 4)\u00b2. Explanation A perfect square trinomial is a specific type of quadratic expression that is the result of squaring a binomial. There are […]<\/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-266812","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266812","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=266812"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266812\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=266812"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=266812"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=266812"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}