Factor completely 4×4\u221224×3+36×2.
A) 4×2(x\u22123)2
B) 4(x\u22123)2
C) 4×2(x+3)(x\u22123) <\/p>\n\n\n\n
D) 4x(x2\u22126x+9)<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To factor the expression ( 4x^4 – 24x^3 + 36x^2 ) completely, we start by identifying the common factors in each term.<\/p>\n\n\n\n The given polynomial consists of three terms:<\/p>\n\n\n\n We observe that each term has a factor of ( 4x^2 ). Thus, we can factor ( 4x^2 ) out of the entire expression:<\/p>\n\n\n\n [ Next, we need to factor the quadratic expression ( x^2 – 6x + 9 ). To do this, we look for two numbers that multiply to ( 9 ) (the constant term) and add to ( -6 ) (the coefficient of ( x )). The numbers ( -3 ) and ( -3 ) satisfy both conditions because:<\/p>\n\n\n\n [ Thus, we can rewrite the quadratic as:<\/p>\n\n\n\n [ Now substituting back into the expression, we have:<\/p>\n\n\n\n [ Thus, the completely factored form of the original expression ( 4x^4 – 24x^3 + 36x^2 ) is:<\/p>\n\n\n\n [ To verify, we can expand ( 4x^2(x – 3)^2 ) back to see if we obtain the original expression:<\/p>\n\n\n\n [ [ Since the expansion matches the original expression, the factoring is confirmed to be correct. The answer is option A: ( 4x^2(x – 3)^2 )<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" Factor completely 4×4\u221224×3+36×2.A) 4×2(x\u22123)2B) 4(x\u22123)2C) 4×2(x+3)(x\u22123) D) 4x(x2\u22126x+9) The Correct Answer and Explanation is: To factor the expression ( 4x^4 – 24x^3 + 36x^2 ) completely, we start by identifying the common factors in each term. Step 1: Identify Common Factors The given polynomial consists of three terms: We observe that each term has a […]<\/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-160438","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160438","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=160438"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/160438\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=160438"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=160438"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=160438"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Identify Common Factors<\/h3>\n\n\n\n
\n
4x^2(x^2 – 6x + 9)
]<\/p>\n\n\n\nStep 2: Factor the Quadratic Expression<\/h3>\n\n\n\n
-3 \\times -3 = 9
]
[
-3 + -3 = -6
]<\/p>\n\n\n\n
x^2 – 6x + 9 = (x – 3)(x – 3) = (x – 3)^2
]<\/p>\n\n\n\nStep 3: Combine the Factors<\/h3>\n\n\n\n
4x^2(x^2 – 6x + 9) = 4x^2(x – 3)^2
]<\/p>\n\n\n\nConclusion<\/h3>\n\n\n\n
\\boxed{4x^2(x – 3)^2}
]<\/p>\n\n\n\nVerification<\/h3>\n\n\n\n
\n
(x – 3)(x – 3) = x^2 – 6x + 9
]<\/p>\n\n\n\n\n
4x^2(x^2 – 6x + 9) = 4x^4 – 24x^3 + 36x^2
]<\/p>\n\n\n\n