{"id":10779,"date":"2022-05-30T01:19:05","date_gmt":"2022-05-29T19:49:05","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10779"},"modified":"2022-05-30T01:19:09","modified_gmt":"2022-05-29T19:49:09","slug":"check-whether-the-first-polynomial-is-a-factor-of-the-second-polynomial-by-dividing-the-second-polynomial-by-the-first-polynomial","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/check-whether-the-first-polynomial-is-a-factor-of-the-second-polynomial-by-dividing-the-second-polynomial-by-the-first-polynomial\/","title":{"rendered":"Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial :"},"content":{"rendered":"

Question<\/strong> : Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial :<\/p>\n

(i)<\/strong>\u00a0 \\(t^2 – 3\\) ; \\(2t^4 + 3t^3 – 2t^2 – 9t – 12\\)<\/p>\n

(ii)<\/strong>\u00a0 \\(x^2 + 3x + 1\\) ; \\(3x^4 + 5x^3 – 7x^2 + 2x + 2\\)<\/p>\n

(iii)<\/strong>\u00a0 \\(x^3 – 3x + 1\\) ; \\(x^5 – 4x^4 + x^2 + 3x + 1\\)<\/p>\n

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

(i)<\/strong>\u00a0 Let us divide \\(2t^4 + 3t^3 – 2t^2 – 9t – 12\\) by \\(t^2 – 3\\)<\/p>\n

\"polynomial<\/p>\n

Since the remainder is zero, therefore, \\(t^2 – 3\\) is a factor<\/strong> of \\(2t^4 + 3t^3 – 2t^2 – 9t – 12\\)<\/p>\n

(ii)<\/strong>\u00a0 Let us divide \\(3x^4 + 5x^3 – 7x^2 + 2x + 2\\) by \\(x^2 + 3x + 1\\)<\/p>\n

\"polynomial<\/p>\n

Since the remainder is zero, therefore, \\(x^2 + 3x + 1\\)\u00a0is a factor<\/strong> of \\(3x^4 + 5x^3 – 7x^2 + 2x + 2\\)<\/p>\n

(iii)<\/strong>\u00a0 Let us divide \\(x^5 – 4x^4 + x^2 + 3x + 1\\) by \\(x^3 – 3x + 1\\)<\/p>\n

\"polynomial<\/p>\n

Since the remainder is not zero, therefore, \\(x^2 – 3x + 1\\) is not a factor<\/strong> of\u00a0\\(x^5 – 4x^4 + x^2 + 3x + 1\\).<\/p>\n","protected":false},"excerpt":{"rendered":"

Question : Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial : (i)\u00a0 \\(t^2 – 3\\) ; \\(2t^4 + 3t^3 – 2t^2 – 9t – 12\\) (ii)\u00a0 \\(x^2 + 3x + 1\\) ; \\(3x^4 + 5x^3 – 7x^2 + 2x + 2\\) (iii)\u00a0 …<\/p>\n

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial :<\/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":"\nCheck whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial : - 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\/check-whether-the-first-polynomial-is-a-factor-of-the-second-polynomial-by-dividing-the-second-polynomial-by-the-first-polynomial\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial : - 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