To factor the expression \u22124x+24\u22124×2-4x + 24 – 4x^2\u22124x+24\u22124×2 completely, follow these steps:<\/p>\n\n\n\n
Step 1: Rearrange the terms<\/h3>\n\n\n\n
First, rewrite the expression in standard form:\u22124x+24\u22124×2=\u22124×2\u22124x+24-4x + 24 – 4x^2 = -4x^2 – 4x + 24\u22124x+24\u22124×2=\u22124×2\u22124x+24<\/p>\n\n\n\n
Step 2: Factor out the greatest common factor (GCF)<\/h3>\n\n\n\n
The GCF of all the terms is \u22124-4\u22124, so we factor \u22124-4\u22124 out of the entire expression:\u22124(x2+x\u22126)-4(x^2 + x – 6)\u22124(x2+x\u22126)<\/p>\n\n\n\n
Step 3: Factor the quadratic expression<\/h3>\n\n\n\n
Now, we need to factor the quadratic expression x2+x\u22126x^2 + x – 6×2+x\u22126. We need to find two numbers that multiply to \u22126-6\u22126 and add to 111 (the coefficient of the middle term, xxx).<\/p>\n\n\n\n
The two numbers that satisfy these conditions are 333 and \u22122-2\u22122, because:3\u00d7(\u22122)=\u22126and3+(\u22122)=13 \\times (-2) = -6 \\quad \\text{and} \\quad 3 + (-2) = 13\u00d7(\u22122)=\u22126and3+(\u22122)=1<\/p>\n\n\n\n
Thus, we can factor x2+x\u22126x^2 + x – 6×2+x\u22126 as:(x+3)(x\u22122)(x + 3)(x – 2)(x+3)(x\u22122)<\/p>\n\n\n\n
Step 4: Write the completely factored expression<\/h3>\n\n\n\n
Now substitute the factored form of the quadratic back into the expression:\u22124(x+3)(x\u22122)-4(x + 3)(x – 2)\u22124(x+3)(x\u22122)<\/p>\n\n\n\n
Step 5: Final Answer<\/h3>\n\n\n\n
So, the completely factored form of the given expression is:\u22124(x+3)(x\u22122)\\boxed{-4(x + 3)(x – 2)}\u22124(x+3)(x\u22122)\u200b<\/p>\n\n\n\n
Explanation of the Answer<\/h3>\n\n\n\n
We first factored out the GCF, \u22124-4\u22124, and then factored the quadratic expression x2+x\u22126x^2 + x – 6×2+x\u22126 by finding two numbers that multiply to \u22126-6\u22126 and add to 111. This process gave us the factors (x+3)(x + 3)(x+3) and (x\u22122)(x – 2)(x\u22122), which we then combined with the GCF. Therefore, the correct answer is option D:\u22124(x+3)(x\u22122)\\boxed{-4(x + 3)(x – 2)}\u22124(x+3)(x\u22122)\u200b<\/p>\n\n\n\n Factor -4x + 24 – 4x^2 completely. A) (x – 3)(x + 2) B) (x + 3)(x – 2) C) 4(x + 3)(x – 2) D) -4(x + 3)(x – 2 The Correct Answer and Explanation is: To factor the expression \u22124x+24\u22124×2-4x + 24 – 4x^2\u22124x+24\u22124×2 completely, follow these steps: Step 1: Rearrange the terms […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-45771","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45771","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=45771"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45771\/revisions"}],"predecessor-version":[{"id":45773,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45771\/revisions\/45773"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=45771"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=45771"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=45771"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-71.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"