Page 1 Q u e s t i o n : 7 7 Mark the correct alternative in each of the following: If x - 2 is a factor of x 2 + 3ax - 2a, then a = a 2 b - 2 c 1 d -1 S o l u t i o n : As is a factor of i.e. Hence, correct option is d. Q u e s t i o n : 7 8 If x 3 + 6x 2 + 4x + k is exactly divisible by x + 2, then k = a -6 Page 2 Q u e s t i o n : 7 7 Mark the correct alternative in each of the following: If x - 2 is a factor of x 2 + 3ax - 2a, then a = a 2 b - 2 c 1 d -1 S o l u t i o n : As is a factor of i.e. Hence, correct option is d. Q u e s t i o n : 7 8 If x 3 + 6x 2 + 4x + k is exactly divisible by x + 2, then k = a -6 b -7 c -8 d -10 S o l u t i o n : As is exactly divisible by i.e., is a factor of f(x). Therefore, Hence, the correct option is c. Q u e s t i o n : 7 9 If x - a is a factor of x 3 -3x 2 a + 2a 2 x + b, then the value of b is a 0 b 2 c 1 d 3 S o l u t i o n : As is a factor of i.e. Thus, b = 0 Thus, the correct option is a. Q u e s t i o n : 8 0 If x 140 + 2x 151 + k is divisible by x + 1, then the value of k is a 1 b -3 c 2 d -2 S o l u t i o n : As is divisible by i.e., is a factor of f(x). Therefore, Hence, the correct option is a. Q u e s t i o n : 8 1 If x + 2 is a factor of x 2 + mx + 14, then m = a 7 b 2 c 9 d 14 S o l u t i o n : Page 3 Q u e s t i o n : 7 7 Mark the correct alternative in each of the following: If x - 2 is a factor of x 2 + 3ax - 2a, then a = a 2 b - 2 c 1 d -1 S o l u t i o n : As is a factor of i.e. Hence, correct option is d. Q u e s t i o n : 7 8 If x 3 + 6x 2 + 4x + k is exactly divisible by x + 2, then k = a -6 b -7 c -8 d -10 S o l u t i o n : As is exactly divisible by i.e., is a factor of f(x). Therefore, Hence, the correct option is c. Q u e s t i o n : 7 9 If x - a is a factor of x 3 -3x 2 a + 2a 2 x + b, then the value of b is a 0 b 2 c 1 d 3 S o l u t i o n : As is a factor of i.e. Thus, b = 0 Thus, the correct option is a. Q u e s t i o n : 8 0 If x 140 + 2x 151 + k is divisible by x + 1, then the value of k is a 1 b -3 c 2 d -2 S o l u t i o n : As is divisible by i.e., is a factor of f(x). Therefore, Hence, the correct option is a. Q u e s t i o n : 8 1 If x + 2 is a factor of x 2 + mx + 14, then m = a 7 b 2 c 9 d 14 S o l u t i o n : As is a factor of Therefore, Hence, the correct option is c. Q u e s t i o n : 8 2 If x - 3 is a factor of x 2 - ax - 15, then a = a -2 b 5 c -5 d 3 S o l u t i o n : As is a factor of polynomial i.e. Therefore, Hence, the correct option is a Q u e s t i o n : 8 3 If x 51 + 51 is divided by x + 1, the remainder is a 0 b 1 c 49 d 50 S o l u t i o n : As is divided by The remainder will be Hence, the correct option is d. Q u e s t i o n : 8 4 If x + 1 is a factor of the polynomial 2x 2 + kx, then k = a -2 b -3 c 4 d 2 S o l u t i o n : As is a factor of polynomial Therefore, So, Hence, the correct option is d. Page 4 Q u e s t i o n : 7 7 Mark the correct alternative in each of the following: If x - 2 is a factor of x 2 + 3ax - 2a, then a = a 2 b - 2 c 1 d -1 S o l u t i o n : As is a factor of i.e. Hence, correct option is d. Q u e s t i o n : 7 8 If x 3 + 6x 2 + 4x + k is exactly divisible by x + 2, then k = a -6 b -7 c -8 d -10 S o l u t i o n : As is exactly divisible by i.e., is a factor of f(x). Therefore, Hence, the correct option is c. Q u e s t i o n : 7 9 If x - a is a factor of x 3 -3x 2 a + 2a 2 x + b, then the value of b is a 0 b 2 c 1 d 3 S o l u t i o n : As is a factor of i.e. Thus, b = 0 Thus, the correct option is a. Q u e s t i o n : 8 0 If x 140 + 2x 151 + k is divisible by x + 1, then the value of k is a 1 b -3 c 2 d -2 S o l u t i o n : As is divisible by i.e., is a factor of f(x). Therefore, Hence, the correct option is a. Q u e s t i o n : 8 1 If x + 2 is a factor of x 2 + mx + 14, then m = a 7 b 2 c 9 d 14 S o l u t i o n : As is a factor of Therefore, Hence, the correct option is c. Q u e s t i o n : 8 2 If x - 3 is a factor of x 2 - ax - 15, then a = a -2 b 5 c -5 d 3 S o l u t i o n : As is a factor of polynomial i.e. Therefore, Hence, the correct option is a Q u e s t i o n : 8 3 If x 51 + 51 is divided by x + 1, the remainder is a 0 b 1 c 49 d 50 S o l u t i o n : As is divided by The remainder will be Hence, the correct option is d. Q u e s t i o n : 8 4 If x + 1 is a factor of the polynomial 2x 2 + kx, then k = a -2 b -3 c 4 d 2 S o l u t i o n : As is a factor of polynomial Therefore, So, Hence, the correct option is d. Q u e s t i o n : 8 5 If x + a is a factor of x 4 - a 2 x 2 + 3x - 6a, then a = a 0 b -1 c 1 d 2 S o l u t i o n : As is a factor of polynomial Therefore, Hence, the correct option is a. Q u e s t i o n : 8 6 The value of k for which x - 1 is a factor of 4x 3 + 3x 2 - 4x + k, is a 3 b 1 c -2 d -3 S o l u t i o n : As is a factor of polynomial f(x) = 4x 3 + 3x 2 - 4x + k Therefore, Hence, the correct option is d. Q u e s t i o n : 8 7 If x + 2 and x - 1 are the factors of x 3 + 10x 2 + mx + n, then the values of m and n are respectively a 5 and -3 b 17 and -8 c 7 and -18 d 23 and -19 S o l u t i o n : It is given and are the factors of the polynomial i.e., and Now -8 +40 -2m +n = 0 ? -2m +n = -32 ? 2m -n = 32 . . . (i) And Solving equation i and ii we get Page 5 Q u e s t i o n : 7 7 Mark the correct alternative in each of the following: If x - 2 is a factor of x 2 + 3ax - 2a, then a = a 2 b - 2 c 1 d -1 S o l u t i o n : As is a factor of i.e. Hence, correct option is d. Q u e s t i o n : 7 8 If x 3 + 6x 2 + 4x + k is exactly divisible by x + 2, then k = a -6 b -7 c -8 d -10 S o l u t i o n : As is exactly divisible by i.e., is a factor of f(x). Therefore, Hence, the correct option is c. Q u e s t i o n : 7 9 If x - a is a factor of x 3 -3x 2 a + 2a 2 x + b, then the value of b is a 0 b 2 c 1 d 3 S o l u t i o n : As is a factor of i.e. Thus, b = 0 Thus, the correct option is a. Q u e s t i o n : 8 0 If x 140 + 2x 151 + k is divisible by x + 1, then the value of k is a 1 b -3 c 2 d -2 S o l u t i o n : As is divisible by i.e., is a factor of f(x). Therefore, Hence, the correct option is a. Q u e s t i o n : 8 1 If x + 2 is a factor of x 2 + mx + 14, then m = a 7 b 2 c 9 d 14 S o l u t i o n : As is a factor of Therefore, Hence, the correct option is c. Q u e s t i o n : 8 2 If x - 3 is a factor of x 2 - ax - 15, then a = a -2 b 5 c -5 d 3 S o l u t i o n : As is a factor of polynomial i.e. Therefore, Hence, the correct option is a Q u e s t i o n : 8 3 If x 51 + 51 is divided by x + 1, the remainder is a 0 b 1 c 49 d 50 S o l u t i o n : As is divided by The remainder will be Hence, the correct option is d. Q u e s t i o n : 8 4 If x + 1 is a factor of the polynomial 2x 2 + kx, then k = a -2 b -3 c 4 d 2 S o l u t i o n : As is a factor of polynomial Therefore, So, Hence, the correct option is d. Q u e s t i o n : 8 5 If x + a is a factor of x 4 - a 2 x 2 + 3x - 6a, then a = a 0 b -1 c 1 d 2 S o l u t i o n : As is a factor of polynomial Therefore, Hence, the correct option is a. Q u e s t i o n : 8 6 The value of k for which x - 1 is a factor of 4x 3 + 3x 2 - 4x + k, is a 3 b 1 c -2 d -3 S o l u t i o n : As is a factor of polynomial f(x) = 4x 3 + 3x 2 - 4x + k Therefore, Hence, the correct option is d. Q u e s t i o n : 8 7 If x + 2 and x - 1 are the factors of x 3 + 10x 2 + mx + n, then the values of m and n are respectively a 5 and -3 b 17 and -8 c 7 and -18 d 23 and -19 S o l u t i o n : It is given and are the factors of the polynomial i.e., and Now -8 +40 -2m +n = 0 ? -2m +n = -32 ? 2m -n = 32 . . . (i) And Solving equation i and ii we get m = 7 and n = - 18 Hence, the correct option is c Q u e s t i o n : 8 8 Let f(x) be a polynomial such that f - 1 2 = 0, then a factor of f(x) is a 2x - 1 b 2x + 1 c x - 1 d x + 1 S o l u t i o n : Let f(x) be a polynomial such that i.e., is a factor. On rearranging can be written as Thus, is a factor of f(x). Hence, the correct option is b. Q u e s t i o n : 8 9 When x 3 - 2x 2 + ax - b is divided by x 2 - 2x - 3, the remainder is x - 6. The values of a and b are respectively a -2, -6 b 2 and -6 c -2 and 6 d 2 and 6 S o l u t i o n : If the reminder (x -6) is subtracted from the given polynomial then rest of part of this polynomial is exactly divisible by x 2 - 2x - 3. Therefore, Now, Therefore, are factors of polynomial p(x). Now, And and Solving i and ii we get Hence, the correct option is c. Q u e s t i o n : 9 0 One factor of x 4 + x 2 - 20 is x 2 + 5. The other factor is a ( )Read More

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