2<\/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 \nHere, the remainder is 0.<\/p>\n(ii) By long division, we have: \n \nHere, the remainder is \\(\\frac{27}{8}\\)<\/p>\n
(iii) By long division, we have \n \nHere, the remainder is 1<\/p>\n
<\/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 \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 \nHere, remainder is \\(-\\frac{27}{8}\\)<\/p>\nQuestion 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 <\/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 \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 \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n