{"id":223277,"date":"2025-06-01T12:07:59","date_gmt":"2025-06-01T12:07:59","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=223277"},"modified":"2025-06-01T12:08:01","modified_gmt":"2025-06-01T12:08:01","slug":"what-isin-factored-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/01\/what-isin-factored-form\/","title":{"rendered":"What isin factored form"},"content":{"rendered":"\n

What is
in factored form?<\/p>\n\n\n\n

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

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

We are asked to factor the polynomial: 12×3\u22129×2\u22124x+312x^3 – 9x^2 – 4x + 3<\/p>\n\n\n\n

Step-by-step Factoring by Grouping:<\/h3>\n\n\n\n

1. Group terms:<\/strong><\/p>\n\n\n\n

Group the terms in pairs: (12×3\u22129×2)+(\u22124x+3)(12x^3 – 9x^2) + (-4x + 3)<\/p>\n\n\n\n

2. Factor out the greatest common factor (GCF) from each group:<\/strong><\/p>\n\n\n\n

From the first group 12×3\u22129x212x^3 – 9x^2, the GCF is 3x23x^2: 3×2(4x\u22123)3x^2(4x – 3)<\/p>\n\n\n\n

From the second group \u22124x+3-4x + 3, we factor out \u22121-1: \u22121(4x\u22123)-1(4x – 3)<\/p>\n\n\n\n

So we now have: 3×2(4x\u22123)\u22121(4x\u22123)3x^2(4x – 3) – 1(4x – 3)<\/p>\n\n\n\n

3. Factor out the common binomial factor (4x\u22123)(4x – 3):<\/strong> (3×2\u22121)(4x\u22123)(3x^2 – 1)(4x – 3)<\/p>\n\n\n\n

\n\n\n\n

Final Answer:<\/h3>\n\n\n\n

(3×2\u22121)(4x\u22123)\\boxed{(3x^2 – 1)(4x – 3)}<\/p>\n\n\n\n

\n\n\n\n

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

Factoring by grouping is a method used to factor polynomials with four terms. It involves grouping terms in pairs, factoring out the greatest common factor from each group, and then factoring out a common binomial factor.<\/p>\n\n\n\n

In the polynomial 12×3\u22129×2\u22124x+312x^3 – 9x^2 – 4x + 3, we first group the terms: (12×3\u22129×2)(12x^3 – 9x^2) and (\u22124x+3)(-4x + 3). These groupings allow us to see a common factor within each pair.<\/p>\n\n\n\n

From the first group 12×3\u22129x212x^3 – 9x^2, the common factor is 3x23x^2. Factoring this gives 3×2(4x\u22123)3x^2(4x – 3). In the second group \u22124x+3-4x + 3, we factor out \u22121-1 to get \u22121(4x\u22123)-1(4x – 3).<\/p>\n\n\n\n

Now both groups share a common binomial factor (4x\u22123)(4x – 3), which can be factored out, resulting in (3×2\u22121)(4x\u22123)(3x^2 – 1)(4x – 3).<\/p>\n\n\n\n

This shows the expression has been successfully factored. You can verify the result by expanding the factored form using the distributive property: (3×2\u22121)(4x\u22123)=3×2(4x)\u22123×2(3)\u22121(4x)+1(3)=12×3\u22129×2\u22124x+3(3x^2 – 1)(4x – 3) = 3x^2(4x) – 3x^2(3) – 1(4x) + 1(3) = 12x^3 – 9x^2 – 4x + 3<\/p>\n\n\n\n

which matches the original polynomial. Factoring is a powerful algebraic tool, helping simplify expressions and solve equations more easily.<\/p>\n\n\n\n

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

What isin factored form? The Correct Answer and Explanation is: We are asked to factor the polynomial: 12×3\u22129×2\u22124x+312x^3 – 9x^2 – 4x + 3 Step-by-step Factoring by Grouping: 1. Group terms: Group the terms in pairs: (12×3\u22129×2)+(\u22124x+3)(12x^3 – 9x^2) + (-4x + 3) 2. Factor out the greatest common factor (GCF) from each group: From […]<\/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-223277","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223277","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=223277"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/223277\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=223277"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=223277"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=223277"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}