{"id":62160,"date":"2023-09-05T04:32:00","date_gmt":"2023-09-04T23:02:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=62160"},"modified":"2023-11-23T10:15:36","modified_gmt":"2023-11-23T04:45:36","slug":"rd-sharma-solutions-class-9-maths-chapter-6-factorization-of-polynomials","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/","title":{"rendered":"RD Sharma Solutions Class 9 Maths Chapter 6 &#8211; Factorization of Polynomials (Updated for 2024)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-124419\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solutions-Class-9-Maths-Chapter-6-Factorization-Of-Polynomials.png\" alt=\"RD Sharma Solutions Class 9 Maths Chapter 6\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solutions-Class-9-Maths-Chapter-6-Factorization-Of-Polynomials.png 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solutions-Class-9-Maths-Chapter-6-Factorization-Of-Polynomials-768x432.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><span style=\"font-weight: 400;\"><strong>RD Sharma Solutions Class 9 Maths Chapter 6 Factorization Of Polynomials:<\/strong> The best solution for all your factorization of polynomials practices which happens to be the most important topic in the CBSE Class 9 Algebra syllabus in Mathematics. The section teaches you the steps to factor a polynomial. You can start practicing the <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 9 Maths<\/a> Chapter 6 and ace your Class 9 Maths exam.\u00a0<\/span><\/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-69e72c07231c8\" 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-69e72c07231c8\"><\/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-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/#download-rd-sharma-solutions-class-9-maths-chapter-6-pdf\" title=\"Download RD Sharma Solutions Class 9 Maths Chapter 6\u00a0 PDF\">Download RD Sharma Solutions Class 9 Maths Chapter 6\u00a0 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-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/#exercise-wise-rd-sharma-solutions-class-9-maths-chapter-6\" title=\"Exercise-wise: RD Sharma Solutions Class 9 Maths Chapter 6\u00a0\">Exercise-wise: RD Sharma Solutions Class 9 Maths Chapter 6\u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/#access-answers-of-rd-sharma-solutions-class-9-maths-chapter-6-%e2%80%93-factorization-of-polynomials\" title=\"Access answers of RD Sharma Solutions Class 9 Maths Chapter 6 &#8211; Factorization of Polynomials\">Access answers of RD Sharma Solutions Class 9 Maths Chapter 6 &#8211; Factorization of Polynomials<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/#rd-sharma-class-9-solutions-chapter-6-factorisation-of-polynomials-ex-61\" title=\"RD Sharma Class 9 Solutions Chapter 6 Factorisation of Polynomials Ex 6.1\">RD Sharma Class 9 Solutions Chapter 6 Factorisation of Polynomials Ex 6.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/#exercise-61-page-no-62\" title=\"Exercise 6.1 Page No: 6.2\">Exercise 6.1 Page No: 6.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/#exercise-62-page-no-68\" title=\"Exercise 6.2 Page No: 6.8\">Exercise 6.2 Page No: 6.8<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/#important-topics-rd-sharma-cbse-class-9-chapter-6\" title=\"Important Topics RD Sharma CBSE Class 9 Chapter 6\">Important Topics RD Sharma CBSE Class 9 Chapter 6<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/#rd-sharma-solutions-class-9-maths-chapter-6-%e2%80%93-factorization-of-polynomials\" title=\"RD Sharma Solutions Class 9 Maths Chapter 6 &#8211; Factorization of Polynomials\">RD Sharma Solutions Class 9 Maths Chapter 6 &#8211; Factorization of Polynomials<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/#from-where-can-i-download-the-pdf-of-rd-sharma-solutions-class-9-maths-chapter-6\" title=\"From where can I download the PDF of RD Sharma Solutions Class 9 Maths Chapter 6?\">From where can I download the PDF of RD Sharma Solutions Class 9 Maths Chapter 6?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/#how-much-does-it-cost-to-download-the-pdf-of-rd-sharma-solutions-for-class-9-maths-chapter-6\" title=\"How much does it cost to download the PDF of RD Sharma Solutions for Class 9 Maths Chapter 6?\">How much does it cost to download the PDF of RD Sharma Solutions for Class 9 Maths Chapter 6?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/#can-i-access-the-rd-sharma-solutions-for-class-9-maths-chapter-6-pdf-offline\" title=\"Can I access the RD Sharma Solutions for Class 9 Maths Chapter 6\u00a0PDF offline?\">Can I access the RD Sharma Solutions for Class 9 Maths Chapter 6\u00a0PDF offline?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-solutions-class-9-maths-chapter-6-pdf\"><\/span><strong>Download RD Sharma Solutions Class 9 Maths Chapter 6\u00a0 PDF<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/09\/rd-6-1.pdf\">RD Sharma Solutions Class 9 Maths Chapter 6<\/a><\/p>\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\/09\/rd-6-1.pdf\", \"#example1\");<\/script><\/p>\n<h2><span class=\"ez-toc-section\" id=\"exercise-wise-rd-sharma-solutions-class-9-maths-chapter-6\"><\/span><strong>Exercise-wise: RD Sharma Solutions Class 9 Maths Chapter 6\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 100%;\"><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-6-class-9-maths-exercise-6-1-solutions\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 9 Chapter 6 Exercise 6.1<\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;\"><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-6-class-9-maths-exercise-6-2-solutions\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 9 Chapter 6 Exercise 6.2<\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;\"><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-6-class-9-maths-exercise-6-3-solutions\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 9 Chapter 6 Exercise 6.3<\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;\"><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-6-class-9-maths-exercise-6-4-solutions\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 9 Chapter 6 Exercise 6.4<\/a><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;\"><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-6-class-9-maths-exercise-6-5-solutions\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 9 Chapter 6 Exercise 6.5<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><span class=\"ez-toc-section\" id=\"access-answers-of-rd-sharma-solutions-class-9-maths-chapter-6-%e2%80%93-factorization-of-polynomials\"><\/span><strong>Access answers of RD Sharma Solutions Class 9 Maths Chapter 6 &#8211; Factorization of Polynomials<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"rd-sharma-class-9-solutions-chapter-6-factorisation-of-polynomials-ex-61\"><\/span>RD Sharma Class 9 Solutions Chapter 6 Factorisation of Polynomials Ex 6.1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"exercise-61-page-no-62\"><\/span>Exercise 6.1 Page No: 6.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Question 1: Which of the following expressions are polynomials in one variable, and which are not? State reasons for your answer:<\/strong><\/p>\n<p><strong>(i) 3x<sup>2<\/sup>\u00a0\u2013 4x + 15<\/strong><\/p>\n<p><strong>(ii) y<sup>2<\/sup>\u00a0+ 2\u221a3<\/strong><\/p>\n<p><strong>(iii) 3\u221ax + \u221a2x<\/strong><\/p>\n<p><strong>(iv) x \u2013 4\/x<\/strong><\/p>\n<p><strong>(v) x<sup>12<\/sup>\u00a0+ y<sup>3<\/sup>\u00a0+ t<sup>50<\/sup><\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)<\/strong>\u00a03x<sup>2<\/sup>\u00a0\u2013 4x + 15<\/p>\n<p><em>It is a polynomial of x.<\/em><\/p>\n<p><strong>(ii)<\/strong>\u00a0y<sup>2<\/sup>\u00a0+ 2\u221a3<\/p>\n<p><em>It is a polynomial of y.<\/em><\/p>\n<p><strong>(iii)<\/strong>\u00a03\u221ax + \u221a2x<\/p>\n<p><em>It is not a polynomial since the exponent of 3\u221ax is a rational term.<\/em><\/p>\n<p><strong>(iv)<\/strong>\u00a0x \u2013 4\/x<\/p>\n<p><em>It is not a polynomial since the exponent of \u2013 4\/x is not a positive term.<\/em><\/p>\n<p><strong>(v)<\/strong>\u00a0x<sup>12<\/sup>\u00a0+ y<sup>3<\/sup>\u00a0+ t<sup>50<\/sup><\/p>\n<p><em>It is a three-variable polynomial, x, y and t.<\/em><\/p>\n<p><strong>Question 2: Write the coefficient of x<sup>2<\/sup>\u00a0in each of the following:<\/strong><\/p>\n<p><strong>(i) 17 \u2013 2x + 7x<sup>2<\/sup><\/strong><\/p>\n<p><strong>(ii) 9 \u2013 12x + x<sup>3<\/sup><\/strong><\/p>\n<p><strong>(iii) \u220f\/6 x<sup>2<\/sup>\u00a0\u2013 3x + 4<\/strong><\/p>\n<p><strong>(iv) \u221a3x \u2013 7<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)<\/strong>\u00a017 \u2013 2x + 7x<sup>2<\/sup><\/p>\n<p><em>Coefficient of x<sup>2<\/sup>\u00a0= 7<\/em><\/p>\n<p><strong>(ii)<\/strong>\u00a09 \u2013 12x + x<sup>3<\/sup><\/p>\n<p><em>Coefficient of x<sup>2\u00a0<\/sup>=0<\/em><\/p>\n<p><strong>(iii)<\/strong>\u00a0\u220f\/6 x<sup>2<\/sup>\u00a0\u2013 3x + 4<\/p>\n<p><em>Coefficient of x<sup>2\u00a0<\/sup>= \u220f\/6<\/em><\/p>\n<p><strong>(iv)<\/strong>\u00a0\u221a3x \u2013 7<\/p>\n<p><em>Coefficient of x<sup>2\u00a0<\/sup>= 0<\/em><\/p>\n<p><strong>Question 3: Write the degrees of each of the following polynomials:<\/strong><\/p>\n<p><strong>(i) 7x<sup>3<\/sup>\u00a0+ 4x<sup>2<\/sup>\u00a0\u2013 3x + 12<\/strong><\/p>\n<p><strong>(ii) 12 \u2013 x + 2x<sup>3<\/sup><\/strong><\/p>\n<p><strong>(iii) 5y \u2013 \u221a2<\/strong><\/p>\n<p><strong>(iv) 7<\/strong><\/p>\n<p><strong>(v) 0<\/strong><\/p>\n<p><strong>Solution<\/strong>:<\/p>\n<p>As we know, degree is the highest power in the polynomial<\/p>\n<p><strong>(i)<\/strong>\u00a0Degree of the polynomial 7x<sup>3<\/sup>\u00a0+ 4x<sup>2<\/sup>\u00a0\u2013 3x + 12 is\u00a0<em>3<\/em><\/p>\n<p><strong>(ii)<\/strong>\u00a0Degree of the polynomial 12 \u2013 x + 2x<sup>3<\/sup>\u00a0is\u00a0<em>3<\/em><\/p>\n<p><strong>(iii)<\/strong>\u00a0Degree of the polynomial 5y \u2013 \u221a2 is\u00a0<em>1<\/em><\/p>\n<p><strong>(iv)<\/strong>\u00a0Degree of the polynomial 7 is\u00a0<em>0<\/em><\/p>\n<p><strong>(v)<\/strong>\u00a0Degree of the polynomial 0 is\u00a0<em>undefined.<\/em><\/p>\n<p><strong>Question 4: Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:<\/strong><\/p>\n<p><strong>(i) x + x<sup>2<\/sup>\u00a0+ 4<\/strong><\/p>\n<p><strong>(ii) 3x \u2013 2<\/strong><\/p>\n<p><strong>(iii) 2x + x<sup>2<\/sup><\/strong><\/p>\n<p><strong>(iv) 3y<\/strong><\/p>\n<p><strong>(v) t<sup>2<\/sup>\u00a0+ 1<\/strong><\/p>\n<p><strong>(vi) 7t<sup>4<\/sup>\u00a0+ 4t<sup>3<\/sup>\u00a0+ 3t \u2013 2<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)<\/strong>\u00a0x + x<sup>2<\/sup>\u00a0+ 4: It is a quadratic polynomial as its degree is\u00a0<em>2<\/em>.<\/p>\n<p><strong>(ii)<\/strong>\u00a03x \u2013 2 : It is a linear polynomial as its degree is\u00a0<em>1<\/em>.<\/p>\n<p><strong>(iii)<\/strong>\u00a02x + x<sup>2<\/sup>: It is a quadratic polynomial as its degree is\u00a0<em>2<\/em>.<\/p>\n<p><strong>(iv)<\/strong>\u00a03y: It is a linear polynomial as its degree is\u00a0<em>1<\/em>.<\/p>\n<p><strong>(v)<\/strong>\u00a0t<sup>2<\/sup>+ 1: It is a quadratic polynomial as its degree is\u00a0<em>2<\/em>.<\/p>\n<p><strong>(vi)<\/strong>\u00a07t<sup>4<\/sup>\u00a0+ 4t<sup>3<\/sup>\u00a0+ 3t \u2013 2: It is a biquadratic polynomial as its degree is\u00a0<em>4<\/em>.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"exercise-62-page-no-68\"><\/span>Exercise 6.2 Page No: 6.8<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Question 1: If f(x) = 2x<sup>3<\/sup>\u00a0\u2013 13x<sup>2<\/sup>\u00a0+ 17x + 12, find<\/strong><\/p>\n<p><strong>(i) f (2)<\/strong><\/p>\n<p><strong>(ii) f (-3)<\/strong><\/p>\n<p><strong>(iii) f(0)<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>f(x) = 2x<sup>3<\/sup>\u00a0\u2013 13x<sup>2<\/sup>\u00a0+ 17x + 12<\/p>\n<p><strong>(i)<\/strong>\u00a0f(2) = 2(2)<sup>3<\/sup>\u00a0\u2013 13(2)<sup>\u00a02<\/sup>\u00a0+ 17(2) + 12<\/p>\n<p>= 2 x 8 \u2013 13 x 4 + 17 x 2 + 12<\/p>\n<p>= 16 \u2013 52 + 34 + 12<\/p>\n<p>= 62 \u2013 52<\/p>\n<p><em>= 10<\/em><\/p>\n<p><strong>(ii)<\/strong>\u00a0f(-3) = 2(-3)<sup>3<\/sup>\u00a0\u2013 13(-3)<sup>\u00a02<\/sup>\u00a0+ 17 x (-3) + 12<\/p>\n<p>= 2 x (-27) \u2013 13 x 9 + 17 x (-3) + 12<\/p>\n<p>= -54 \u2013 117 -51 + 12<\/p>\n<p>= -222 + 12<\/p>\n<p><em>= -210<\/em><\/p>\n<p><strong>(iii)<\/strong>\u00a0f(0) = 2 x (0)<sup>3<\/sup>\u00a0\u2013 13(0)<sup>\u00a02<\/sup>\u00a0+ 17 x 0 + 12<\/p>\n<p>= 0-0 + 0+ 12<\/p>\n<p><em>= 12<\/em><\/p>\n<p><strong>Question 2: Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following cases:<\/strong><\/p>\n<p><strong>(i) f(x) = 3x + 1, x = \u22121\/3<\/strong><\/p>\n<p><strong>(ii) f(x) = x<sup>2<\/sup>\u00a0\u2013 1, x = 1,\u22121<\/strong><\/p>\n<p><strong>(iii) g(x) = 3x<sup>2<\/sup>\u00a0\u2013 2 , x = 2\/\u221a3 , \u22122\/\u221a3<\/strong><\/p>\n<p><strong>(iv) p(x) = x<sup>3<\/sup>\u00a0\u2013 6x<sup>2<\/sup>\u00a0+ 11x \u2013 6 , x = 1, 2, 3<\/strong><\/p>\n<p><strong>(v) f(x) = 5x \u2013 \u03c0, x = 4\/5<\/strong><\/p>\n<p><strong>(vi) f(x) = x<sup>2<\/sup>\u00a0, x = 0<\/strong><\/p>\n<p><strong>(vii) f(x) = lx + m, x = \u2212m\/l<\/strong><\/p>\n<p><strong>(viii) f(x) = 2x + 1, x = 1\/2<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)<\/strong>\u00a0f(x) = 3x + 1, x = \u22121\/3<\/p>\n<p>f(x) = 3x + 1<\/p>\n<p>Substitute x = \u22121\/3 in f(x)<\/p>\n<p>f( \u22121\/3) = 3(\u22121\/3) + 1<\/p>\n<p>= -1 + 1<\/p>\n<p>= 0<\/p>\n<p><em>Since, the result is 0, so x = \u22121\/3 is the root of 3x + 1<\/em><\/p>\n<p><strong>(ii)<\/strong>\u00a0f(x) = x<sup>2<\/sup>\u00a0\u2013 1, x = 1,\u22121<\/p>\n<p>f(x) = x<sup>2<\/sup>\u00a0\u2013 1<\/p>\n<p>Given that x = (1 , -1)<\/p>\n<p>Substitute x = 1 in f(x)<\/p>\n<p>f(1) = 1<sup>2<\/sup>\u00a0\u2013 1<\/p>\n<p>= 1 \u2013 1<\/p>\n<p>= 0<\/p>\n<p>Now, substitute x = (-1) in f(x)<\/p>\n<p>f(-1) = (\u22121)<sup>2<\/sup>\u00a0\u2013 1<\/p>\n<p>= 1 \u2013 1<\/p>\n<p>= 0<\/p>\n<p><em>Since , the results when x = 1 and x = -1 are 0, so (1 , -1) are the roots of the polynomial f(x) = x<sup>2\u00a0<\/sup>\u2013 1<\/em><\/p>\n<p><strong>(iii)<\/strong>\u00a0g(x) = 3x<sup>2<\/sup>\u00a0\u2013 2 , x = 2\/\u221a3 , \u22122\/\u221a3<\/p>\n<p>g(x) = 3x<sup>2<\/sup>\u00a0\u2013 2<\/p>\n<p>Substitute x = 2\/\u221a3 in g(x)<\/p>\n<p>g(2\/\u221a3) = 3(2\/\u221a3)<sup>2<\/sup>\u00a0\u2013 2<\/p>\n<p>= 3(4\/3) \u2013 2<\/p>\n<p>= 4 \u2013 2<\/p>\n<p>= 2 \u2260 0<\/p>\n<p>Now, Substitute x = \u22122\/\u221a3 in g(x)<\/p>\n<p>g(2\/\u221a3) = 3(-2\/\u221a3)<sup>2<\/sup>\u00a0\u2013 2<\/p>\n<p>= 3(4\/3) \u2013 2<\/p>\n<p>= 4 \u2013 2<\/p>\n<p>= 2 \u2260 0<\/p>\n<p><em>The results when x = 2\/\u221a3 and x = \u22122\/\u221a3) are not 0. Therefore, (2\/\u221a3 , \u22122\/\u221a3 ) are not zeros of 3x<sup>2<\/sup>\u20132.<\/em><\/p>\n<p><strong>(iv)<\/strong>\u00a0p(x) = x<sup>3<\/sup>\u00a0\u2013 6x<sup>2<\/sup>\u00a0+ 11x \u2013 6 , x = 1, 2, 3<\/p>\n<p>p(1) = 1<sup>3<\/sup>\u00a0\u2013 6(1)<sup>2<\/sup>\u00a0+ 11x 1 \u2013 6 = 1 \u2013 6 + 11 \u2013 6 = 0<\/p>\n<p>p(2) = 2<sup>3<\/sup>\u00a0\u2013 6(2)<sup>2<\/sup>\u00a0+ 11\u00d72 \u2013 6 = 8 \u2013 24 + 22 \u2013 6 = 0<\/p>\n<p>p(3) = 3<sup>3<\/sup>\u00a0\u2013 6(3)<sup>2<\/sup>\u00a0+ 11\u00d73 \u2013 6 = 27 \u2013 54 + 33 \u2013 6 = 0<\/p>\n<p><em>Therefore, x = 1, 2, 3 are zeros of p(x).<\/em><\/p>\n<p><strong>(v)<\/strong>\u00a0f(x) = 5x \u2013 \u03c0, x = 4\/5<\/p>\n<p>f(4\/5) = 5 x 4\/5 \u2013 \u03c0 = 4 \u2013 \u03c0 \u2260 0<\/p>\n<p><em>Therefore, x = 4\/5 is not a zeros of f(x).<\/em><\/p>\n<p><strong>(vi)<\/strong>\u00a0f(x) = x<sup>2<\/sup>\u00a0, x = 0<\/p>\n<p>f(0) = 0<sup>2<\/sup>\u00a0= 0<\/p>\n<p><em>Therefore, x = 0 is a zero of f(x).<\/em><\/p>\n<p><strong>(vii)<\/strong>\u00a0f(x) = lx + m, x = \u2212m\/l<\/p>\n<p>f(\u2212m\/l) = l x \u2212m\/l + m = -m + m = 0<\/p>\n<p><em>Therefore, x = \u2212m\/l is a zero of f(x).<\/em><\/p>\n<p><strong>(viii)<\/strong>\u00a0f(x) = 2x + 1, x = \u00bd<\/p>\n<p>f(1\/2) = 2x 1\/2 + 1 = 1 + 1 = 2 \u2260 0<\/p>\n<p><em>Therefore, x = \u00bd is not a zero of f(x).<\/em><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-topics-rd-sharma-cbse-class-9-chapter-6\"><\/span><strong>Important Topics RD Sharma CBSE Class 9 Chapter 6<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><span style=\"font-weight: 400;\">With RD Sharma Solutions\u00a0 of Chapter 6 for Class 9, students will get to study the important concepts of Polynomials and Factorization that include:<\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Factorization of Polynomials Introduction<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Terms and coefficients<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Degree of a polynomial<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Types of polynomials<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Remainder Theorem<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">The factorization of polynomials by using the factor theorem<\/span><\/li>\n<\/ul>\n<p>This is the complete blog on RD Sharma Solutions Class 9 Chapter 6. <span style=\"font-weight: 400;\">The solutions come at no cost and help you focus on your study for the <a href=\"https:\/\/cbse.nic.in\/\" target=\"_blank\" rel=\"noopener noreferrer\">CBSE<\/a> class 9 Mathematics exam. To know more about the Class 9 Maths exams, ask in the comments.\u00a0<\/span><\/p>\n<h2><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-9-maths-chapter-6-%e2%80%93-factorization-of-polynomials\"><\/span><strong>RD Sharma Solutions Class 9 Maths Chapter 6 &#8211; Factorization of Polynomials<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u00a0<\/p>\n<p>\u00a0<\/p>\n<p>\u00a0<\/p>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1630666809530\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"from-where-can-i-download-the-pdf-of-rd-sharma-solutions-class-9-maths-chapter-6\"><\/span>From where can I download the PDF of RD Sharma Solutions Class 9 Maths Chapter 6?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can find the download link from the above blog.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630666853249\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-much-does-it-cost-to-download-the-pdf-of-rd-sharma-solutions-for-class-9-maths-chapter-6\"><\/span>How much does it cost to download the PDF of RD Sharma Solutions for Class 9 Maths Chapter 6?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can download it for free.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630666870866\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-access-the-rd-sharma-solutions-for-class-9-maths-chapter-6-pdf-offline\"><\/span>Can I access the RD Sharma Solutions for Class 9 Maths Chapter 6\u00a0PDF offline?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Once you have downloaded the PDF online, you can access it offline as well.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 9 Maths Chapter 6 Factorization Of Polynomials: The best solution for all your factorization of polynomials practices which happens to be the most important topic in the CBSE Class 9 Algebra syllabus in Mathematics. The section teaches you the steps to factor a polynomial. You can start practicing the RD Sharma &#8230; <a title=\"RD Sharma Solutions Class 9 Maths Chapter 6 &#8211; Factorization of Polynomials (Updated for 2024)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-6-factorization-of-polynomials\/\" aria-label=\"More on RD Sharma Solutions Class 9 Maths Chapter 6 &#8211; Factorization of Polynomials (Updated for 2024)\">Read more<\/a><\/p>\n","protected":false},"author":243,"featured_media":124419,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2985,73411,73410],"tags":[3081,3037,3048,3086],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/62160"}],"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\/243"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=62160"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/62160\/revisions"}],"predecessor-version":[{"id":511192,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/62160\/revisions\/511192"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/124419"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=62160"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=62160"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=62160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}