In order to factor 4x ^ 2 – 27x + 18 , we must break up the “bx” term into two terms whose coefficients\u2026
add to-27 and multiply to 72.
add to 27 and multiply to 72.
add to 27 and multiply to 72.
add to 7 and multiply to -72.<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n To factor the quadratic expression 4×2\u221227x+184x^2 – 27x + 18, we need to break up the “bx” term into two parts. The goal is to find two numbers that add up to -27 (the coefficient of xx) and multiply to 72 (the product of 4\u00d7184 \\times 18).<\/p>\n\n\n\n Step 1: Identify the product and sum.<\/strong> We need two numbers that add up to -27 and multiply to 72.<\/p>\n\n\n\n Step 2: Find two numbers that satisfy the conditions.<\/strong> and \u22129\u00d7\u221218=72-9 \\times -18 = 72<\/p>\n\n\n\n Step 3: Break up the “bx” term.<\/strong> Step 4: Factor by grouping.<\/strong> Now, factor out the greatest common factor (GCF) from each group: x(4x\u22129)\u221218(4x\u22129)x(4x – 9) – 18(4x – 9)<\/p>\n\n\n\n Step 5: Factor out the common binomial.<\/strong> Thus, the factored form of 4×2\u221227x+184x^2 – 27x + 18 is: (4x\u22129)(x\u221218)(4x – 9)(x – 18)<\/p>\n\n\n\n The correct answer to the question is “add to -27 and multiply to 72.”<\/p>\n","protected":false},"excerpt":{"rendered":" In order to factor 4x ^ 2 – 27x + 18 , we must break up the “bx” term into two terms whose coefficients\u2026add to-27 and multiply to 72.add to 27 and multiply to 72.add to 27 and multiply to 72.add to 7 and multiply to -72. The correct answer and explanation is: To factor […]<\/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-271805","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271805","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=271805"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271805\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271805"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271805"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271805"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
The coefficient of x2x^2 is 4, and the constant term is 18. Therefore, the product of the first and last coefficients is: 4\u00d718=724 \\times 18 = 72<\/p>\n\n\n\n
We need two numbers that add to -27 and multiply to 72. These numbers are -9 and -18 because: \u22129+(\u221218)=\u221227-9 + (-18) = -27<\/p>\n\n\n\n
Now that we have the two numbers, we can split the middle term, \u221227x-27x, into \u22129x-9x and \u221218x-18x. This gives us: 4×2\u22129x\u221218x+184x^2 – 9x – 18x + 18<\/p>\n\n\n\n
Next, we group the terms: (4×2\u22129x)\u2212(18x\u221218)(4x^2 – 9x) – (18x – 18)<\/p>\n\n\n\n
Since both terms contain (4x\u22129)(4x – 9), we can factor it out: (4x\u22129)(x\u221218)(4x – 9)(x – 18)<\/p>\n\n\n\n