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Page 1 of 9, Mathematics, (Chapter – 2) (Polynomials), (Class - X), Exercise 2.3, Question 1:, Divide the polynomial p(x) by the polynomial g(x) and find the quotient, and remainder in each of the following:, ) P(x) = x' -3x +5x-3,, g(x) = x - 2, (i), (ii) p(x)=x* - 3x +4x+5,, (ii) P(x) = x* - 5x+6,, g(x) = x +1-x, g(x) = 2-x, Answer 1:, (i), p(x)=x -3x +5x-3, q(x) = x² - 2, x-3, x - 2) x' - 3x? +5x- 3, -2.x, -3x + 7x-3, - 3x, +6, 7x -9, Quotient = x - 3, Remainder = 7x - 9, 1| Page

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Page 2 of 9, (ii) p(x)=x' - 3x° +4x+5= x* +0.x° - 3x* + 4x+5, q(x)=x' +1-x=x* -x+l, x²+x-3, x -x+1) x* +0.x - 3x + 4x+5, x + x?, x*-, x -4x + 4.x+5, x* + x, - 3x +3x +5, -3x +3x - 3, 8, Quotient = x² + x - 3, Remainder = 8, 2 | Page

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Page 3 of 9, (iii) p(x) =x*-5.x+ 6 = x* +0.x - 5xr+6, 9(x) = 2-x = -r* +2, -x²-2, x* +0.x - 5x+6, r*- 2x, -x' +2), 2r - 5x+6, -4, -5x +10, Quotient, -x2 - 2, %D, Remainder = -5x +10, Question 2:, Check whether the first polynomial is a factor of the second polynomial, by dividing the second polynomial by the first polynomial:, (i) -3,2r' +31' –21 -91-12, (ii) x' +3x+1,3r' +5x' -7x+2x+2, (iii) x' - 3.r+1,x' - 4x' + x' + 3x+1, Answer 2:, (i), i-3, 21' +31' - 2r -91-12, 3| Page

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Page 5 of 9, Hence,, x' +3.x+1 is a factor of 3x'+ 5x' - 7.r + 2.x+2., (ii), x'-3x+1, x'-4x'+x' +3x+1, x'-3x+1) x-4x' +x +3x+1, +, -x, +3x+1, -x, +3x -1, +, +, 2, Since the remainder +0,, Hence, -3х +1, is not a factor of x-4x' +r+3x+1, Question 3:, Obtain all other zeroes of 3x +6.r - 2.x-10x-5, if two of its zeroes are, and -, 13, Answer 3:, p(x) = 3x'+6x' -2x-10x-5, Şince the two zeroes are, and, 月-, x+., is a factor of, 3x' +6.x' -2.x -10x-5, Therefore, we divide the given polynomial by x, 3, 5 | Page