{"id":71955,"date":"2021-02-04T15:14:29","date_gmt":"2021-02-04T09:44:29","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=71955"},"modified":"2021-08-18T12:01:23","modified_gmt":"2021-08-18T06:31:23","slug":"rd-sharma-chapter-6-class-9-maths-exercise-6-3-solutions","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-6-class-9-maths-exercise-6-3-solutions\/","title":{"rendered":"RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions"},"content":{"rendered":"\n<p>RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions is based on the Remainder Theorem of Factorization of Polynomial. In this article, we will provide complete detailed information about the remainder theorem and terms related to the Factorization of Polynomial. The remainder theorem of polynomials provides us a connection between the remainder and its dividend.<\/p>\n<p>Moreover, download the RD Sharma Chapter 6 Class 9 Maths Excercise 6.3 Solution PDF for practicing to score well in the exam. Our experts prepare the PDF for the students, which helps them understand this topic of Chapter 6 Class 9. Go down to the article for the detailed information about the im[portant definition of the Remainder Theorem with examples.<\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/\" target=\"_blank\" rel=\"noopener noreferrer\">Click Here<\/a> to know about the Chapter 6 Factorization of Polynomial<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69db72c40ecda\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69db72c40ecda\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-6-class-9-maths-exercise-6-3-solutions\/#download-rd-sharma-chapter-6-class-9-maths-exercise-63-solutions-pdf\" title=\"Download RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions PDF\">Download RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-6-class-9-maths-exercise-6-3-solutions\/#important-definitions-rd-sharma-chapter-6-class-9-maths-exercise-63-solutions\" title=\"Important Definitions RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions\">Important Definitions RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-6-class-9-maths-exercise-6-3-solutions\/#examples-of-remainder-theorem\" title=\"Examples of Remainder Theorem\">Examples of Remainder Theorem<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-6-class-9-maths-exercise-6-3-solutions\/#frequently-asked-questions-faqs-of-rd-sharma-chapter-6-class-9-maths-exercise-63-solutions\" title=\"Frequently Asked Questions (FAQs) of RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions\">Frequently Asked Questions (FAQs) of RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-chapter-6-class-9-maths-exercise-63-solutions-pdf\"><\/span>Download RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/Solutions-for-Class-9-Maths-Chapter-6-Factorization-of-Polynomials-Exercise-6.3.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/Solutions-for-Class-9-Maths-Chapter-6-Factorization-of-Polynomials-Exercise-6.3.pdf\">Solutions for Class 9 Maths Chapter 6 Factorization of Polynomials Exercise 6.3<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-definitions-rd-sharma-chapter-6-class-9-maths-exercise-63-solutions\"><\/span>Important Definitions RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The remainder theorem of polynomials provides us a link between the remainder and its dividend. Let f(p) be any polynomial of degree greater than or equal to one and \u2018a\u2019 be any real number. If f(p) is divided by the linear polynomial p \u2013 a, then the remainder is f(a).<\/p>\n<p>So fundamentally, p -a is the divisor of f(p) if and only if f(a) = 0. It is applied to factorize polynomials of each degree in a simple manner.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"examples-of-remainder-theorem\"><\/span>Examples of Remainder Theorem<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ques- Find the root of the polynomial x2\u2212 3x\u2013 4.<\/strong><\/p>\n<p><strong>Solution-<\/strong> x2\u2013 3x\u2013 4<\/p>\n<p>= f(4) = 42\u2013 3(4)\u2013 4<\/p>\n<p>= f(4)=16\u201316=0<\/p>\n<p>So,\u00a0 (x-4) must be a factor of x2\u2013 3x\u2013 4<\/p>\n<p><strong>Ques- f(x) = 9x<sup>3<\/sup> \u2013 3x<sup>2<\/sup> + x \u2013 5, g(x) = x \u2013 2\/3<\/strong><\/p>\n<p><strong>Solution-<\/strong><\/p>\n<p>f(x) = 9x<sup>3<\/sup> \u2013 3x<sup>2<\/sup> + x \u2013 5, g(x) = x \u2013 2\/3<\/p>\n<p>Put g(x) = 0<\/p>\n<p>= x \u2013 2\/3 = 0 or x = 2\/3<\/p>\n<p>Remainder = f(2\/3)<\/p>\n<p>Now,<\/p>\n<p>f(2\/3) = 9(2\/3)<sup>3<\/sup> \u2013 3(2\/3)<sup>2<\/sup> + (2\/3) \u2013 5 = 8\/3 \u2013 4\/3 + 2\/3 \u2013 5\/1 = -3<\/p>\n<p><strong>Ques- f(x) = 2x<sup>4<\/sup> \u2013 6X<sup>3<\/sup> + 2x<sup>2<\/sup> \u2013 x + 2, g(x) = x + 2<\/strong><\/p>\n<p><strong>Solution-<\/strong><\/p>\n<p>f(x) = 2x<sup>4<\/sup> \u2013 6X<sup>3<\/sup> + 2x<sup>2<\/sup> \u2013 x + 2, g(x) = x + 2<\/p>\n<p>Put g(x) = 0<\/p>\n<p>= x + 2 = 0 or x = -2<\/p>\n<p>Remainder = f(-2)<\/p>\n<p>Now,<\/p>\n<p>f(-2) = 2(-2)<sup>4<\/sup> \u2013 6(-2)<sup>3<\/sup> + 2(-2)<sup>2<\/sup> \u2013 (-2) + 2 = 32 + 48 + 8 + 2 + 2 = 92<\/p>\n<h2><span class=\"ez-toc-section\" id=\"frequently-asked-questions-faqs-of-rd-sharma-chapter-6-class-9-maths-exercise-63-solutions\"><\/span>Frequently Asked Questions (FAQs) of RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Ques 1- How does remainder theorem work?<\/strong><\/p>\n<p><strong>Ans-<\/strong>If you divide a polynomial, f(x), by linear identity, x-A, the remainder will be similar as f(A). For example, the remainder when is divided by x-3 is.<\/p>\n<p><strong>Ques 2- What happens if the remainder is zero?<\/strong><\/p>\n<p><strong>Ans-<\/strong> When the remainder is zero, both the quotient and divisor are the factors of dividend. But, when the remainder is not zero, neither the quotient nor the divisor is the factor of the dividend.<\/p>\n<p><strong>Ques- How do you find the quotient and remainder?<\/strong><\/p>\n<p><strong>Ans-<\/strong> Finding Dividend, divisor, quotient, and the remainder from the following expressions-<\/p>\n<p>a\/n = q + r\/n<\/p>\n<ol>\n<li><strong>a<\/strong> is the first number to divide, known as the <strong>dividend<\/strong>.<\/li>\n<li><strong>n<\/strong> is the number divide by; it is known as the <strong>divisor<\/strong>.<\/li>\n<li><strong>q <\/strong>is the result of division turned down to the nearest integer; it is known as the <strong>quotient<\/strong>.<\/li>\n<li><strong>r<\/strong> is the remainder of the mathematical operation.<\/li>\n<\/ol>\n<p><a href=\"https:\/\/cbse.gov.in\/\" target=\"_blank\" rel=\"noopener noreferrer\">Know about CBSE Board<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions is based on the Remainder Theorem of Factorization of Polynomial. In this article, we will provide complete detailed information about the remainder theorem and terms related to the Factorization of Polynomial. The remainder theorem of polynomials provides us a connection between the remainder and its &#8230; <a title=\"RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-6-class-9-maths-exercise-6-3-solutions\/\" aria-label=\"More on RD Sharma Chapter 6 Class 9 Maths Exercise 6.3 Solutions\">Read more<\/a><\/p>\n","protected":false},"author":241,"featured_media":71956,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2985,2917,73719,73411],"tags":[3081,3086,3085],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/71955"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/241"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=71955"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/71955\/revisions"}],"predecessor-version":[{"id":116317,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/71955\/revisions\/116317"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/71956"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=71955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=71955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=71955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}