If (x – 2) and (x + 1) are factors of the expression x

^{3}+ px^{2}+ qx + 1, what is the sum of p and q-
**A.**

9 -
**B.**

-3 -
**C.**

3 -
**D.**

(frac{17}{3}) -
**E.**

(frac{2}{3})

##### Correct Answer: Option B

##### Explanation

x^{3} + px^{2} + qx + 1 = (x – 1) Q(x) + R

x – 2 = 0, x = 2, R = 0,

4p + 2p = -9……..(i)

x^{3} + px^{2} + qx + 1 = (x – 1)Q(x) + R

-1 + p – q + 1 = 0

p – q = 0…….(ii)

Solve the equation simultaneously

p = (frac{-3}{2})

q = (frac{-3}{2})

p + q = (frac{3}{2}) – (frac{3}{2})

= (frac{-6}{2})

= -3