To divide x3\u22124x+6x+3\\frac{x^3 – 4x + 6}{x+3}x+3×3\u22124x+6\u200b, we will use polynomial long division. Here\u2019s the step-by-step process:<\/p>\n\n\n\n
Step 1: Set up the division<\/h3>\n\n\n\n
We want to divide x3\u22124x+6x^3 – 4x + 6×3\u22124x+6 by x+3x + 3x+3. Start by setting it up like a regular division problem:Dividend: x3+0x2\u22124x+6\\text{Dividend: } x^3 + 0x^2 – 4x + 6Dividend: x3+0x2\u22124x+6Divisor: x+3\\text{Divisor: } x + 3Divisor: x+3<\/p>\n\n\n\n
Step 2: Divide the first term<\/h3>\n\n\n\n
Divide the first term of the dividend, x3x^3×3, by the first term of the divisor, xxx. This gives:x3x=x2\\frac{x^3}{x} = x^2xx3\u200b=x2<\/p>\n\n\n\n
Write x2x^2×2 as the first term of the quotient.<\/p>\n\n\n\n
Step 3: Multiply and subtract<\/h3>\n\n\n\n
Now, multiply x2x^2×2 by the divisor x+3x + 3x+3 and subtract the result from the dividend:x2\u22c5(x+3)=x3+3x2x^2 \\cdot (x + 3) = x^3 + 3x^2×2\u22c5(x+3)=x3+3×2<\/p>\n\n\n\n
Subtract x3+3x2x^3 + 3x^2×3+3×2 from the dividend x3+0x2\u22124x+6x^3 + 0x^2 – 4x + 6×3+0x2\u22124x+6:(x3+0x2\u22124x+6)\u2212(x3+3×2)=\u22123×2\u22124x+6(x^3 + 0x^2 – 4x + 6) – (x^3 + 3x^2) = -3x^2 – 4x + 6(x3+0x2\u22124x+6)\u2212(x3+3×2)=\u22123×2\u22124x+6<\/p>\n\n\n\n
Step 4: Divide the next term<\/h3>\n\n\n\n
Now, divide \u22123×2-3x^2\u22123×2 by xxx, which gives:\u22123x2x=\u22123x\\frac{-3x^2}{x} = -3xx\u22123×2\u200b=\u22123x<\/p>\n\n\n\n
Write \u22123x-3x\u22123x as the next term in the quotient.<\/p>\n\n\n\n
Step 5: Multiply and subtract again<\/h3>\n\n\n\n
Multiply \u22123x-3x\u22123x by the divisor x+3x + 3x+3 and subtract:\u22123x\u22c5(x+3)=\u22123×2\u22129x-3x \\cdot (x + 3) = -3x^2 – 9x\u22123x\u22c5(x+3)=\u22123×2\u22129x<\/p>\n\n\n\n
Subtract \u22123×2\u22129x-3x^2 – 9x\u22123×2\u22129x from \u22123×2\u22124x+6-3x^2 – 4x + 6\u22123×2\u22124x+6:(\u22123×2\u22124x+6)\u2212(\u22123×2\u22129x)=5x+6(-3x^2 – 4x + 6) – (-3x^2 – 9x) = 5x + 6(\u22123×2\u22124x+6)\u2212(\u22123×2\u22129x)=5x+6<\/p>\n\n\n\n
Step 6: Divide the next term<\/h3>\n\n\n\n
Next, divide 5x5x5x by xxx, which gives:5xx=5\\frac{5x}{x} = 5x5x\u200b=5<\/p>\n\n\n\n
Write 555 as the next term in the quotient.<\/p>\n\n\n\n
Step 7: Multiply and subtract<\/h3>\n\n\n\n
Multiply 555 by x+3x + 3x+3 and subtract:5\u22c5(x+3)=5x+155 \\cdot (x + 3) = 5x + 155\u22c5(x+3)=5x+15<\/p>\n\n\n\n
Subtract 5x+155x + 155x+15 from 5x+65x + 65x+6:(5x+6)\u2212(5x+15)=\u22129(5x + 6) – (5x + 15) = -9(5x+6)\u2212(5x+15)=\u22129<\/p>\n\n\n\n
Step 8: Write the final result<\/h3>\n\n\n\n
Now, we have no more terms left to divide by xxx. Therefore, the quotient is:x2\u22123x+5x^2 – 3x + 5×2\u22123x+5<\/p>\n\n\n\n
And the remainder is \u22129-9\u22129. Thus, the final result is:x3\u22124x+6x+3=x2\u22123x+5+\u22129x+3\\frac{x^3 – 4x + 6}{x + 3} = x^2 – 3x + 5 + \\frac{-9}{x+3}x+3×3\u22124x+6\u200b=x2\u22123x+5+x+3\u22129\u200b<\/p>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
x2\u22123x+5\u22129x+3\\boxed{x^2 – 3x + 5 – \\frac{9}{x+3}}x2\u22123x+5\u2212x+39\u200b\u200b<\/p>\n\n\n\n
This is the complete quotient with the remainder written as a fraction.<\/p>\n\n\n\n Divide. Show your work. \\frac{x^3 – 4x + 6}{x+3} The Correct Answer and Explanation is: To divide x3\u22124x+6x+3\\frac{x^3 – 4x + 6}{x+3}x+3×3\u22124x+6\u200b, we will use polynomial long division. Here\u2019s the step-by-step process: Step 1: Set up the division We want to divide x3\u22124x+6x^3 – 4x + 6×3\u22124x+6 by x+3x + 3x+3. Start by setting it […]<\/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-245638","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245638","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=245638"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245638\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245638"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245638"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245638"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-679.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"