{"id":10517,"date":"2022-04-24T01:01:33","date_gmt":"2022-04-23T19:31:33","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10517"},"modified":"2022-04-24T01:01:36","modified_gmt":"2022-04-23T19:31:36","slug":"divide-the-polynomial-px-by-the-polynomial-gx-and-find-the-quotient-and-remainder-in-each-given-of-the-following","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/divide-the-polynomial-px-by-the-polynomial-gx-and-find-the-quotient-and-remainder-in-each-given-of-the-following\/","title":{"rendered":"Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each given of the following :"},"content":{"rendered":"

Question<\/strong> : Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each given of the following :<\/p>\n

(i)<\/strong>\u00a0 p(x) = \\(x^3 – 3x^2 + 5x – 3\\),\u00a0 g(x) = \\(x^2 – 2\\)<\/p>\n

(ii)<\/strong>\u00a0 p(x) = \\(x^4 – 3x^2 + 4x + 5\\), g(x) = \\(x^2 + 1 – x\\)<\/p>\n

(iii)<\/strong>\u00a0 p(x) = \\(x^4 – 5x + 6\\),\u00a0 g(x) = \\(2 – x^2\\)<\/p>\n

Solution<\/strong> :<\/p>\n

(i)<\/strong>\u00a0 Here, dividend and divisor are both in standard forms. So, we have :<\/p>\n

\"\"<\/p>\n

\\(\\therefore\\)\u00a0 The quotient is x – 3<\/strong> and the remainder is 7x – 9<\/strong><\/p>\n

(ii)<\/strong>\u00a0 Here, dividend is already in standard form and the divisor is not in the standard form. It can be written as \\(x^2 – x + 1\\). We have :<\/p>\n

\"\"<\/p>\n

\\(\\therefore\\)\u00a0 The quotient is \\(x^2 + x – 3\\)<\/strong> and the remainder is 8.<\/strong><\/p>\n

(iii)<\/strong> Here, dividend and divisor are both in standard forms. So, we have :<\/p>\n

\"\"<\/p>\n

\\(\\therefore\\)\u00a0 The quotient is \\(-x^2 – 2\\)<\/strong> and the remainder is -5x + 10.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Question : Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each given of the following : (i)\u00a0 p(x) = \\(x^3 – 3x^2 + 5x – 3\\),\u00a0 g(x) = \\(x^2 – 2\\) (ii)\u00a0 p(x) = \\(x^4 – 3x^2 + 4x + 5\\), g(x) = \\(x^2 + 1 – x\\) …<\/p>\n

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each given of the following :<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,910],"tags":[],"yoast_head":"\nDivide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each given of the following : - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/divide-the-polynomial-px-by-the-polynomial-gx-and-find-the-quotient-and-remainder-in-each-given-of-the-following\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each given of the following : - 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