Which expression represents -8×2 + 54x + 140 in factored form?<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n To factor the expression \u22128×2+54x+140-8x^2 + 54x + 140, let’s go through the process step by step.<\/p>\n\n\n\n The first thing to do is to identify the GCF of all the terms in the expression. The terms are \u22128×2-8x^2, 54x54x, and 140140.<\/p>\n\n\n\n \u22128×2+54x+140=\u22122(4×2\u221227x\u221270)-8x^2 + 54x + 140 = -2(4x^2 – 27x – 70)<\/p>\n\n\n\n Now, we need to focus on factoring the quadratic expression 4×2\u221227x\u2212704x^2 – 27x – 70.<\/p>\n\n\n\n Next, we factor 4×2\u221227x\u2212704x^2 – 27x – 70. To factor this, we will look for two numbers that multiply to 4\u00d7\u221270=\u22122804 \\times -70 = -280 and add up to \u221227-27.<\/p>\n\n\n\n The pair of numbers that works are 77 and \u221240-40, since: 7\u00d7(\u221240)=\u2212280and7+(\u221240)=\u2212277 \\times (-40) = -280 \\quad \\text{and} \\quad 7 + (-40) = -27<\/p>\n\n\n\n Now, we can split the middle term \u221227x-27x using 7x7x and \u221240x-40x: 4×2\u221227x\u221270=4×2+7x\u221240x\u2212704x^2 – 27x – 70 = 4x^2 + 7x – 40x – 70<\/p>\n\n\n\n Now, group the terms in pairs: (4×2+7x)\u2212(40x+70)(4x^2 + 7x) – (40x + 70)<\/p>\n\n\n\n Factor each group: x(4x+7)\u221210(4x+7)x(4x + 7) – 10(4x + 7)<\/p>\n\n\n\n Now, factor out the common binomial factor 4x+74x + 7: x(4x+7)\u221210(4x+7)=(x\u221210)(4x+7)x(4x + 7) – 10(4x + 7) = (x – 10)(4x + 7)<\/p>\n\n\n\n Now, don\u2019t forget the \u22122-2 that we factored out in Step 1. So the fully factored form of the expression is: \u22122(x\u221210)(4x+7)-2(x – 10)(4x + 7)<\/p>\n\n\n\n The expression \u22128×2+54x+140-8x^2 + 54x + 140 in factored form is: \u22122(x\u221210)(4x+7)-2(x – 10)(4x + 7)<\/p>\n\n\n\n To summarize the process, we first identified the greatest common factor (GCF) and factored that out, reducing the quadratic expression to a more manageable form. Then we used factoring by grouping to split and combine the terms. The result was a factored form that reveals the roots of the equation, which are the values of xx that make the expression equal to zero when set equal to zero.<\/p>\n","protected":false},"excerpt":{"rendered":" Which expression represents -8×2 + 54x + 140 in factored form? The correct answer and explanation is: To factor the expression \u22128×2+54x+140-8x^2 + 54x + 140, let’s go through the process step by step. Step 1: Factor out the greatest common factor (GCF) The first thing to do is to identify the GCF of all […]<\/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-240359","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240359","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=240359"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240359\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=240359"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=240359"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=240359"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Factor out the greatest common factor (GCF)<\/h3>\n\n\n\n
\n
Step 2: Factor the quadratic expression<\/h3>\n\n\n\n
Step 3: Split the middle term<\/h3>\n\n\n\n
Step 4: Factor by grouping<\/h3>\n\n\n\n
Step 5: Factor out the common binomial<\/h3>\n\n\n\n
Step 6: Combine with the factor outside the parentheses<\/h3>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
Explanation:<\/h3>\n\n\n\n