Faelyn grouped the terms and factored the GCF out of the groups of the polynomial 6×4 \u2013 8×2 + 3×2 + 4. Her work is shown.
Step 1: (6×4 \u2013 8×2) + (3×2 + 4)<\/p>\n\n\n\n
Step 2: 2×2(3×2 \u2013 4) + 1(3×2 + 4)<\/p>\n\n\n\n
Faelyn noticed that she does not have a common factor. Which accurately describes what Faelyn should do next?<\/p>\n\n\n\n
Faelyn should realize that her work shows that the polynomial is prime.
Faelyn should go back and regroup the terms in Step 1 as (6×4 + 3×2) \u2013 (8×2 + 4).
In Step 2, Faelyn should factor only 2x out of the first expression.
Falyn should factor out a negative from one of the groups so the binomials will be the same.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The correct next step is:<\/p>\n\n\n\n Faelyn should factor out a negative from one of the groups so the binomials will be the same.<\/strong><\/p>\n\n\n\n Let’s analyze the problem in detail.<\/p>\n\n\n\n Faelyn’s polynomial is:<\/p>\n\n\n\n [ She grouped the polynomial as follows:<\/p>\n\n\n\n [ This is a reasonable first step, but now we need to focus on factoring the greatest common factor (GCF) from each group.<\/p>\n\n\n\n Faelyn factored out the GCF from each group:<\/p>\n\n\n\n [ At this stage, there\u2019s an issue. The two binomials ( (3x^2 – 4) ) and ( (3x^2 + 4) ) are not the same, meaning Faelyn cannot combine these terms or factor further unless both binomials match.<\/p>\n\n\n\n Faelyn needs to manipulate the terms to make the two binomials identical. The way to achieve this is by factoring out a negative<\/strong> from one of the groups.<\/p>\n\n\n\n Let’s examine this:<\/p>\n\n\n\n [ If we factor out a negative from the first group, we get:<\/p>\n\n\n\n [ Now, the two binomials are ( (3x^2 – 4) ) and ( (3x^2 + 4) ), which are not<\/strong> the same.<\/p>\n\n\n\n However, the binomial within the parentheses of the second term (3x\u00b2 + 4) can be factored<\/strong> so that the two binomials match. Since we’re factoring in a negative from the first group, we can group them together.<\/p>\n","protected":false},"excerpt":{"rendered":" Faelyn grouped the terms and factored the GCF out of the groups of the polynomial 6×4 \u2013 8×2 + 3×2 + 4. Her work is shown.Step 1: (6×4 \u2013 8×2) + (3×2 + 4) Step 2: 2×2(3×2 \u2013 4) + 1(3×2 + 4) Faelyn noticed that she does not have a common factor. Which accurately […]<\/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-166216","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166216","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=166216"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/166216\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=166216"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=166216"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=166216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Explanation:<\/h3>\n\n\n\n
6x^4 – 8x^2 + 3x^2 + 4
]<\/p>\n\n\n\nStep 1: Group the terms<\/h3>\n\n\n\n
(6x^4 – 8x^2) + (3x^2 + 4)
]<\/p>\n\n\n\nStep 2: Factor out the GCF<\/h3>\n\n\n\n
2x^2(3x^2 – 4) + 1(3x^2 + 4)
]<\/p>\n\n\n\nWhat should Faelyn do next?<\/h3>\n\n\n\n
(6x^4 – 8x^2) + (3x^2 + 4)
]<\/p>\n\n\n\n
-2x^2(3x^2 – 4) + 1(3x^2 + 4)
]<\/p>\n\n\n\n