{"id":24657,"date":"2021-06-19T16:59:03","date_gmt":"2021-06-19T11:29:03","guid":{"rendered":"https:\/\/mcq-questions.com\/?p=24657"},"modified":"2022-03-02T10:38:13","modified_gmt":"2022-03-02T05:08:13","slug":"ncert-solutions-for-class-9-maths-chapter-2-ex-2-3","status":"publish","type":"post","link":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3"},"content":{"rendered":"

These NCERT Solutions for Class 9 Maths<\/a> Chapter 2 Polynomials Ex 2.3 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.3<\/h2>\n

Question 1.
\nFind the remainder when x3<\/sup> + 3x2<\/sup> + 3x + 1 is divided by
\n(i) x + 1
\n(ii) x – \\(\\frac{1}{2}\\)
\n(iii) x
\n(iv) x + p
\n(v) 5 + 2x
\nSolution:
\n(i) By long division, we have:
\n\"NCERT
\nHere, the remainder is 0.<\/p>\n

(ii) By long division, we have:
\n\"NCERT
\nHere, the remainder is \\(\\frac{27}{8}\\)<\/p>\n

(iii) By long division, we have
\n\"NCERT
\nHere, the remainder is 1<\/p>\n

\"NCERT<\/p>\n

(iv) we have given
\nx3<\/sup> + 3x2<\/sup> + 3x + 1 \u00f7 x + \u03c0
\nor, x3<\/sup> + 3x2<\/sup> + 3x + 1 \u00f7 x + \\(\\frac{22}{7}\\) (\u2235 \u03c0 = \\(\\frac{22}{7}\\))
\nBy long division,
\n\"NCERT
\nHere, the remainder is \\(-\\frac{3669}{49}\\)<\/p>\n

(v) We have given
\nx3<\/sup> + 3x2<\/sup> + 3x + 1 \u00f7 5 + 2x
\nor, x3<\/sup> + 3x2<\/sup> + 3x + 1 \u00f7 2x + 5
\nBy long division, we have
\n\"NCERT
\nHere, remainder is \\(-\\frac{27}{8}\\)<\/p>\n

Question 2.
\nFind the remainder when x3<\/sup> – ax2<\/sup> + 6x – a is divided by x – a.
\nSolution:
\nHere, p(x) = x3<\/sup> – ax2<\/sup> + 6x – a, and the zero of x – a is a
\nSo, p(a) = a3<\/sup> – a(a)2<\/sup> + 6(a) – a
\n= a3<\/sup> – a3<\/sup> + 6a – a
\n= 5a
\nSo, 5a is the remainder when x3<\/sup> – ax + 6x – a is divided by x – a.<\/p>\n

\"NCERT<\/p>\n

Question 3.
\nCheck whether 7 + 3x is a factor of 3x3<\/sup> + 7x.
\nSolution:
\nWe know that 7 + 3x is a factor of 3x3<\/sup> + 7x only if 7 + 3x divides 3x3<\/sup> + 7x leaving no remainder.
\nHere, p(x) = 3x3<\/sup> + 7x and the zero of 7 + 3x is \\(-\\frac{7}{3}\\). so,
\n\"NCERT
\nHere, the remainder is \\(\\frac{-490}{9}\\).
\nTherefore 7 + 3x is not the factor of 3x3<\/sup> + 7x.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.3 Question 1. Find the remainder when x3 + 3×2 + 3x + 1 is divided by (i) x + 1 (ii) …<\/p>\n

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","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":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[6],"tags":[],"yoast_head":"\nNCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 - MCQ Questions<\/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:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 - MCQ Questions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.3 Question 1. Find the remainder when x3 + 3x2 + 3x + 1 is divided by (i) x + 1 (ii) … NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ Questions\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/\" \/>\n<meta property=\"article:published_time\" content=\"2021-06-19T11:29:03+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-03-02T05:08:13+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/06\/NCERT-Solutions-for-Class-9-Maths-Chapter-2-Polynomials-Ex-2.3-Q1.png\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:site\" content=\"@ncertsolguru\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasanna\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mcq-questions.com\/#website\",\"url\":\"https:\/\/mcq-questions.com\/\",\"name\":\"MCQ Questions\",\"description\":\"MCQ Questions for Class 1 to 12\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mcq-questions.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/i1.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/06\/NCERT-Solutions-for-Class-9-Maths-Chapter-2-Polynomials-Ex-2.3-Q1.png?fit=271%2C181&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/06\/NCERT-Solutions-for-Class-9-Maths-Chapter-2-Polynomials-Ex-2.3-Q1.png?fit=271%2C181&ssl=1\",\"width\":271,\"height\":181,\"caption\":\"NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 Q1\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/#webpage\",\"url\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/\",\"name\":\"NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 - MCQ Questions\",\"isPartOf\":{\"@id\":\"https:\/\/mcq-questions.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/#primaryimage\"},\"datePublished\":\"2021-06-19T11:29:03+00:00\",\"dateModified\":\"2022-03-02T05:08:13+00:00\",\"author\":{\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\"},\"breadcrumb\":{\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mcq-questions.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3\"}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3\",\"name\":\"Prasanna\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/mcq-questions.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"caption\":\"Prasanna\"},\"url\":\"https:\/\/mcq-questions.com\/author\/prasanna\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 - MCQ Questions","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:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 - MCQ Questions","og_description":"These NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Exercise 2.3 Question 1. Find the remainder when x3 + 3x2 + 3x + 1 is divided by (i) x + 1 (ii) … NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 Read More »","og_url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/","og_site_name":"MCQ Questions","article_publisher":"https:\/\/www.facebook.com\/NCERTSolutionsGuru\/","article_published_time":"2021-06-19T11:29:03+00:00","article_modified_time":"2022-03-02T05:08:13+00:00","og_image":[{"url":"https:\/\/mcq-questions.com\/wp-content\/uploads\/2021\/06\/NCERT-Solutions-for-Class-9-Maths-Chapter-2-Polynomials-Ex-2.3-Q1.png"}],"twitter_card":"summary_large_image","twitter_creator":"@ncertsolguru","twitter_site":"@ncertsolguru","twitter_misc":{"Written by":"Prasanna","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebSite","@id":"https:\/\/mcq-questions.com\/#website","url":"https:\/\/mcq-questions.com\/","name":"MCQ Questions","description":"MCQ Questions for Class 1 to 12","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mcq-questions.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/#primaryimage","inLanguage":"en-US","url":"https:\/\/i1.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/06\/NCERT-Solutions-for-Class-9-Maths-Chapter-2-Polynomials-Ex-2.3-Q1.png?fit=271%2C181&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mcq-questions.com\/wp-content\/uploads\/2021\/06\/NCERT-Solutions-for-Class-9-Maths-Chapter-2-Polynomials-Ex-2.3-Q1.png?fit=271%2C181&ssl=1","width":271,"height":181,"caption":"NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 Q1"},{"@type":"WebPage","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/#webpage","url":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/","name":"NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3 - MCQ Questions","isPartOf":{"@id":"https:\/\/mcq-questions.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/#primaryimage"},"datePublished":"2021-06-19T11:29:03+00:00","dateModified":"2022-03-02T05:08:13+00:00","author":{"@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3"},"breadcrumb":{"@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mcq-questions.com\/ncert-solutions-for-class-9-maths-chapter-2-ex-2-3\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mcq-questions.com\/"},{"@type":"ListItem","position":2,"name":"NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.3"}]},{"@type":"Person","@id":"https:\/\/mcq-questions.com\/#\/schema\/person\/4ba9570f32f2057e70e670c7885e47f3","name":"Prasanna","image":{"@type":"ImageObject","@id":"https:\/\/mcq-questions.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","caption":"Prasanna"},"url":"https:\/\/mcq-questions.com\/author\/prasanna\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/24657"}],"collection":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/comments?post=24657"}],"version-history":[{"count":1,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/24657\/revisions"}],"predecessor-version":[{"id":34181,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/posts\/24657\/revisions\/34181"}],"wp:attachment":[{"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/media?parent=24657"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/categories?post=24657"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mcq-questions.com\/wp-json\/wp\/v2\/tags?post=24657"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}