{"id":10803,"date":"2022-05-30T02:12:08","date_gmt":"2022-05-29T20:42:08","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10803"},"modified":"2022-05-30T02:12:11","modified_gmt":"2022-05-29T20:42:11","slug":"give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/","title":{"rendered":"Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and"},"content":{"rendered":"

Question<\/strong> : Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and<\/p>\n

(i)<\/strong>\u00a0 deg p(x) = deg q(x)<\/p>\n

(ii)<\/strong>\u00a0 deg q(x) = deg r(x)<\/p>\n

(iii)<\/strong>\u00a0 deg q(x) = 0<\/p>\n

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

(i)<\/strong>\u00a0 Let q(x) = \\(3x^2 + 2x + 6\\),\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of q(x) = 2<\/p>\n

p(x) = \\(12x^2 + 8x + 24\\),\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of p(x) = 2<\/p>\n

Here, deg p(x) = deg q(x)<\/strong><\/p>\n

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

q(x) = \\(x^2 + x + 1\\),\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of q(x) = 2<\/p>\n

g(x) = \\(x^3 + x^2 + x + 1\\)<\/p>\n

r(x) = \\(2x^2 – 2x + 1\\),\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of r(x) = 2<\/p>\n

Here, deg q(x) = deg r(x)<\/strong><\/p>\n

(iii)<\/strong>\u00a0 Let p(x) = \\(2x^4 + 8x^3 + 6x^2 + 4x + 12\\),<\/p>\n

q(x) = 2,\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of q(x) = 0<\/p>\n

g(x) = \\(x^4 + 4x^3 + 3x^2 + 2x + 1\\)<\/p>\n

r(x) = 10<\/p>\n

Here, deg q(x) = 0<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Question : Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and (i)\u00a0 deg p(x) = deg q(x) (ii)\u00a0 deg q(x) = deg r(x) (iii)\u00a0 deg q(x) = 0 Solution : (i)\u00a0 Let q(x) = \\(3x^2 + 2x + 6\\),\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of q(x) …<\/p>\n

Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and<\/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":"\nGive examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and - 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\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Question : Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and (i)\u00a0 deg p(x) = deg q(x) (ii)\u00a0 deg q(x) = deg r(x) (iii)\u00a0 deg q(x) = 0 Solution : (i)\u00a0 Let q(x) = (3x^2 + 2x + 6),\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of q(x) … Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2022-05-29T20:42:08+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-05-29T20:42:11+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and\",\"datePublished\":\"2022-05-29T20:42:08+00:00\",\"dateModified\":\"2022-05-29T20:42:11+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/\"},\"wordCount\":146,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Maths Questions\",\"Polynomial Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/\",\"url\":\"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/\",\"name\":\"Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and - Mathemerize\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2022-05-29T20:42:08+00:00\",\"dateModified\":\"2022-05-29T20:42:11+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and - Mathemerize","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/","og_locale":"en_US","og_type":"article","og_title":"Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and - Mathemerize","og_description":"Question : Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and (i)\u00a0 deg p(x) = deg q(x) (ii)\u00a0 deg q(x) = deg r(x) (iii)\u00a0 deg q(x) = 0 Solution : (i)\u00a0 Let q(x) = (3x^2 + 2x + 6),\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Degree of q(x) … Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and Read More »","og_url":"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/","og_site_name":"Mathemerize","article_published_time":"2022-05-29T20:42:08+00:00","article_modified_time":"2022-05-29T20:42:11+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and","datePublished":"2022-05-29T20:42:08+00:00","dateModified":"2022-05-29T20:42:11+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/"},"wordCount":146,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Maths Questions","Polynomial Questions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/","url":"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/","name":"Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and - Mathemerize","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2022-05-29T20:42:08+00:00","dateModified":"2022-05-29T20:42:11+00:00","breadcrumb":{"@id":"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/give-examples-of-polynomials-px-gx-qx-and-rx-which-satisfy-the-division-algorithm-and\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm and"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/10803"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=10803"}],"version-history":[{"count":1,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/10803\/revisions"}],"predecessor-version":[{"id":10804,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/10803\/revisions\/10804"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=10803"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=10803"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=10803"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}