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ID : ww-9-Polynomials [1] Grade 9 Polynomials For more such worksheets visit www.edugain.com Answer t he quest ions (1) If x75 + 75 is divided by (x - 1), f ind the remainder. (2) If f (x) = ax2 + bx + c, and f (1) = 7 and f (-1) = 4, then f ind the value of a + c. (3) If -3x2 + kx - 8 = ( -3x + 4)(x - 2), f ind the value of k. (4) If f (q) = q2 + 4q + 1, the value of f (2q) + f (-q) = ? (5) If , f ind the value of . (6) Find multiplication of zeroes of polynomial y2 - 2y - 48. (7) Find sum of zeroes of polynomial -p2 + 12p - 32. Choose correct answer(s) f rom given choice (8) If f (x) = 7x + 6, f ind the inverse of f , f -1. a. f -1(x) = c. f -1(x) = 1 7x+6 x- 6 7 b. f -1(x) = x- 6 d. f -1(x) = 7x + 6 7 (9) If , f ind value of x3 - y3. a. 1 b. 0 c. -1 d. 2 Fill in t he blanks (10) If (x - 2) is a f actor of kx4 - 2x3 + x2 + x + 26, the value of k = (11) If x3 + 2x2 + 2x + 9 is divide by x + 2, the remainder = (C) 2016 Edugain (www.Edugain.com) . . Personal use only, commercial use is strictly prohibited ID : ww-9-Polynomials [2] Check True/False (12) (x - 2) is a f actor of -x4 - x3 + x2 - x + 23. T rue False © 2016 Edugain (www.edugain.com). All Rights Reserved (C) 2016 Edugain (www.Edugain.com) Many more such worksheets can be generated at www.edugain.com Personal use only, commercial use is strictly prohibited ID : ww-9-Polynomials [3] Answers (1) 76 (2) 5.5 Step 1 f (1) = 7 a(12) + b(1) + c = 7 a + b + c = 7 ______________ (1) Step 2 Similarly f (-1) = 4 a(-12) + b(-1) + c = 4 a - b + c = 4 ______________ (2) Step 3 On adding eq. (1) and (2) 2a + 2c = 11 a + c = 5.5 (3) 10 Step 1 T he given equation is: -3x2 + kx - 8 = ( -3x + 4)(x - 2) ⇒ -3x2 + kx - 8 = -3x2 + 10x - 8 ⇒ kx = 10x ⇒ k = 10 Step 2 T hus, the value of k is 10. (4) 5q2 + 4q + 2 Step 1 It is given that, f (q) = q2 + 4q + 1 T heref ore, f (2q) = (2q)2 + 4(2q) + 1 = 4q2 + 8q + 1, and f (-q) = (-q)2 + 4(-q) + 1 = q2 - 4q + 1 Step 2 Now, f (2q) + f (-q) = 4q2 + 8q + 1 + q2 - 4q + 1 = 5q2 + 4q + 2 (C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited ID : ww-9-Polynomials [4] (5) 8 Step 1 It is given that, . T heref ore, f (2√3) = 2(2√3)2 - 3√3(2√3) + 2 = 24 -18 + 2 =8 Step 2 T hus, the value of is 8. (6) -48 (7) 12 (8) c. f -1(x) = x- 6 7 Step 1 f (x) = 7x + 6 x = [f (x) - 6]/7 Step 2 T heref ore f -1(x) = x- 6 7 (9) b. 0 Step 1 It is given that, ⇒ x2 + y2 = -1 xy ⇒ x2 + y2 = xy ⇒ x2 + y2 + xy = 0 ------(1) Step 2 Now, x3 - y3 can be written as: (x - y)(x2 + xy + y2) = (x - y)(0) ...[From equation (1)] =0 Step 3 T heref ore, the value of x3 - y3 is 0. (C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited ID : ww-9-Polynomials [5] (10) -1 Step 1 We have been told that (x - 2) is a f actor of kx4 - 2x3 + x2 + x + 26. T hus, when the value of (x - 2) is zero, the value of the polynomial kx4 - 2x3 + x2 + x + 26 must also be zero. Step 2 T he value of (x - 2) will be zero when x = 2. T hus, if we put x = 2 in the given polynomial, we can equate it to zero and solve the equation to f ind the value of k: k(2)4 - 2(2)3 + (2)2 + (2) + 26 = 0 ⇒ k = -1 Step 3 T hus, the value of k is -1. (11) 5 (12) False Step 1 Let's assume (x - 2) is a f actor of -x4 - x3 + x2 - x + 23. Step 2 (x - 2) being a f actor, when (x - 2) is zero, the polynomial -x4 - x3 + x2 - x + 23 must also be equal to zero. In other words, when x = 2, the polynomial -x4 - x3 + x2 - x + 23 must also be equal to zero. Step 3 Let us put the value of x as 2 in the given polynomial and see if its value becomes zero or not: p(x) = -x4 - x3 + x2 - x + 23, p(2) = -(2)4 - (2)3 + (2)2 - (2) + 23 = 1 Step 4 Since, p(2) ≠ 0, (x - 2) is not a f actor of -x4 - x3 + x2 - x + 23. Step 5 Hence, the given statement is False. (C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited