Factor 6×4 \u2013 5×2 + 12×2 \u2013 10 by grouping. What is the resulting expression? (6x + 5)(x2 \u2013 2) (6x \u2013 5)(x2 + 2) (6×2 + 5)(x2 \u2013 2) (6×2 \u2013 5)(x2 + 2)<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n We are given the expression: 6×4\u22125×2+12×2\u2212106x^4 – 5x^2 + 12x^2 – 10<\/p>\n\n\n\n Group the terms into two binomials: (6×4\u22125×2)+(12×2\u221210)(6x^4 – 5x^2) + (12x^2 – 10)<\/p>\n\n\n\n Factor out the greatest common factor (GCF) from each group.<\/p>\n\n\n\n x2(6×2\u22125)x^2(6x^2 – 5)<\/p>\n\n\n\n 2(6×2\u22125)2(6x^2 – 5)<\/p>\n\n\n\n So now the expression becomes: x2(6×2\u22125)+2(6×2\u22125)x^2(6x^2 – 5) + 2(6x^2 – 5)<\/p>\n\n\n\n Now that both terms share a common factor of (6×2\u22125)(6x^2 – 5), factor it out: (x2+2)(6×2\u22125)(x^2 + 2)(6x^2 – 5)<\/p>\n\n\n\n This is the fully factored expression.<\/p>\n\n\n\n (6×2\u22125)(x2+2)(6x^2 – 5)(x^2 + 2)<\/p>\n\n\n\n Or rearranged to match the answer choices: (6×2\u22125)(x2+2)(6x^2 – 5)(x^2 + 2)<\/p>\n\n\n\n (6x\u00b2 \u2013 5)(x\u00b2 + 2)<\/strong><\/p>\n\n\n\n Factoring by grouping is a method used when an expression has four terms. The goal is to rearrange and group terms so that you can factor out a common binomial from both groups. In the expression 6×4\u22125×2+12×2\u2212106x^4 – 5x^2 + 12x^2 – 10, start by grouping the terms in pairs: (6×4\u22125×2)+(12×2\u221210)(6x^4 – 5x^2) + (12x^2 – 10)<\/p>\n\n\n\n From the first group, notice that both terms share a factor of x2x^2, so we factor it out: x2(6×2\u22125)x^2(6x^2 – 5)<\/p>\n\n\n\n In the second group, both terms share a factor of 2: 2(6×2\u22125)2(6x^2 – 5)<\/p>\n\n\n\n Now we have: x2(6×2\u22125)+2(6×2\u22125)x^2(6x^2 – 5) + 2(6x^2 – 5)<\/p>\n\n\n\n The binomial (6×2\u22125)(6x^2 – 5) is common to both terms, so we factor it out: (6×2\u22125)(x2+2)(6x^2 – 5)(x^2 + 2)<\/p>\n\n\n\n This is the factored form of the original expression. This method simplifies higher-order polynomials and is especially useful when direct factoring isn\u2019t obvious. The key is recognizing common patterns and carefully factoring out the GCF from each group.<\/p>\n\n\n\n So, the correct answer is (6x\u00b2 \u2013 5)(x\u00b2 + 2)<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" Factor 6×4 \u2013 5×2 + 12×2 \u2013 10 by grouping. What is the resulting expression? (6x + 5)(x2 \u2013 2) (6x \u2013 5)(x2 + 2) (6×2 + 5)(x2 \u2013 2) (6×2 \u2013 5)(x2 + 2) The correct answer and explanation is: We are given the expression: 6×4\u22125×2+12×2\u2212106x^4 – 5x^2 + 12x^2 – 10 Step 1: […]<\/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-18054","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18054","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=18054"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18054\/revisions"}],"predecessor-version":[{"id":18055,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18054\/revisions\/18055"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=18054"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=18054"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=18054"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Group the terms<\/h3>\n\n\n\n
Step 2: Factor each group<\/h3>\n\n\n\n
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Step 3: Factor by grouping<\/h3>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
Correct Option:<\/h3>\n\n\n\n
\n\n\n\nExplanation (300 words):<\/h3>\n\n\n\n