# DIVIDING POLYNOMIALS WITH UNKNOWN COEFFICIENS WORKSHEET

Problem 1 :

If y = 1 is a zero of the polynomial

q(y) = 4y3 + ky2 - y - 1

then find the value of k.

Solution

Problem 2 :

For what value of m is x3 - 2mx2 + 16 is divisible by x + 2.

Solution

Problem 3 :

The polynomials x3 + 2x2 - 5ax - 7 and x3 + ax2 - 12x + 6 when divided by x + 1 and x - 2 respectively, leave remainders R1 and R2 respectively. Find the value of a in each of the following cases :

i) R1 = R2

ii) R1 + R2 = 0

iii) 2R1 + R2 = 0

Solution

Problem 4 :

When a polynomial

p(x) = x4 - 2x3 + 3x2 - ax + b

is divisible by x - 1 and x + 1, the remainders are 5 and 19 respectively. Find the remainder when p(x) is divided by x - 2.

Solution

Problem 5 :

If x - 3 and x - 1/3 are both factors of ax2 + 5x + b, show that a = b.

1)  k = -2

2)  m = 1

3) i) When R1 = R2 ==> a = -4

ii) R1 + R2 = 0 ==> a = 16/9

iii) 2R1 + R2 = 0 ==> a = 11/7

4)  Values of a and b are 5 and 8 respectively.

p(2) = 10

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