{"id":35170,"date":"2025-06-24T07:50:24","date_gmt":"2025-06-24T07:50:24","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=35170"},"modified":"2025-06-24T07:50:27","modified_gmt":"2025-06-24T07:50:27","slug":"x3%e2%88%927x213x3%c3%b7x%e2%88%922","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/x3%e2%88%927x213x3%c3%b7x%e2%88%922\/","title":{"rendered":"(x3\u22127×2+13x+3)\u00f7(x\u22122)"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

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

The expression to simplify is:<\/p>\n\n\n\n

(x3\u22127×2+13x+3)\u00f7(x\u22122)(x^3 – 7x^2 + 13x + 3) \\div (x – 2)<\/p>\n\n\n\n

Correct Answer<\/strong>:<\/h3>\n\n\n\n

The result of the division is:<\/p>\n\n\n\n

(x3\u22127×2+13x+3)\u00f7(x\u22122)=x2\u22125x+3+9x\u22122(x^3 – 7x^2 + 13x + 3) \u00f7 (x – 2) = x^2 – 5x + 3 + \\frac{9}{x – 2}<\/p>\n\n\n\n

Explanation<\/strong>:<\/h3>\n\n\n\n

To divide a polynomial by a binomial, we can use polynomial long division.<\/p>\n\n\n\n

First, divide the leading term x3x^3 by the leading term of the divisor xx, which gives x2x^2. Multiply x2x^2 by the divisor x\u22122x – 2, resulting in x3\u22122x2x^3 – 2x^2. Subtracting this from the original expression, we get a new polynomial:<\/p>\n\n\n\n

(x3\u22127×2+13x+3)\u2212(x3\u22122×2)=\u22125×2+13x+3(x^3 – 7x^2 + 13x + 3) – (x^3 – 2x^2) = -5x^2 + 13x + 3<\/p>\n\n\n\n

Next, divide \u22125×2-5x^2 by xx, giving \u22125x-5x. Multiply \u22125x-5x by x\u22122x – 2, yielding \u22125×2+10x-5x^2 + 10x. Subtracting again:<\/p>\n\n\n\n

(\u22125×2+13x+3)\u2212(\u22125×2+10x)=3x+3(-5x^2 + 13x + 3) – (-5x^2 + 10x) = 3x + 3<\/p>\n\n\n\n

Then divide 3x3x by xx, which gives 33. Multiply 33 by x\u22122x – 2 to get 3x\u221263x – 6. Subtract:<\/p>\n\n\n\n

(3x+3)\u2212(3x\u22126)=9(3x + 3) – (3x – 6) = 9<\/p>\n\n\n\n

The remainder is 9. Since this cannot be divided further by x\u22122x – 2, it becomes the fractional term of the final answer.<\/p>\n\n\n\n

Thus, the quotient is x2\u22125x+3x^2 – 5x + 3 with a remainder of 9, making the complete answer:<\/p>\n\n\n\n

x2\u22125x+3+9x\u22122x^2 – 5x + 3 + \\frac{9}{x – 2}<\/p>\n\n\n\n

This technique is crucial for simplifying rational expressions and understanding the behavior of polynomial functions when divided.<\/p>\n\n\n\n

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

The Correct Answer and Explanation is: The expression to simplify is: (x3\u22127×2+13x+3)\u00f7(x\u22122)(x^3 – 7x^2 + 13x + 3) \\div (x – 2) Correct Answer: The result of the division is: (x3\u22127×2+13x+3)\u00f7(x\u22122)=x2\u22125x+3+9x\u22122(x^3 – 7x^2 + 13x + 3) \u00f7 (x – 2) = x^2 – 5x + 3 + \\frac{9}{x – 2} Explanation: To divide a […]<\/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-35170","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35170","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=35170"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35170\/revisions"}],"predecessor-version":[{"id":35173,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35170\/revisions\/35173"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=35170"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=35170"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=35170"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}