When the expression pm

^{2}+ qm + 1 is divided by (m – 1), it has a remainder is 4, Find p and q respectively-
**A.**

2, -1 -
**B.**

-1, 2 -
**C.**

3, -2 -
**D.**

-2, 3

##### Correct Answer: Option B

##### Explanation

pm^{2} + qm + 1 = (m – 1) Q(x) + 2

p(1)^{2} + q(1) + 1 = 2

p + q + 1 = 2

p + q = 1…..(i)

pm^{2} + qm + 1 = (m – 1)Q(x) + 4

p(-1)^{2} + q(-1) + 1 = 4

p – q + 1 = 4

p – q = 3….(ii)

p + q = 1, p – q = -3

2p = -2, p = -1

-1 + q = 1

q = 2