Question

1. Check whether p(x) is a multiple of g(x) or not, where p(x) = x3 – x + 1, g(x) = 2 – 3x.

2. For what value of k is the polynomial 2x4 + 3x3 + 2 kx2 + 3x + 6 exactly divisible by (x +2)

3. If (x- 2) is a factor of 5x2 – kx – 18, then find the value of k.

4. Factorize: x2 + 9x + 18​

Answer 1

Answer:

Let p(x) = 2x

4

+3x

3

+2px

2

+3x+6

By factor theorem, p(x) will be exactly divisible by (x+2) if $$p ( -2) = 0.Now,p(-2) = 2( -2)^4 + 3( -2)^3 + 2p( -2)^2 + 3( -2) + 6= 32 - 24 + 8p - 6 + 6= 8 + 8p$$

Since, p(−2)=0

⇒8+8p=0

⇒8p=0

⇒8p=−8

⇒p=−1