If (x - 2) and (x + 1) are factors of the expression x3 + px2 + 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 is B

x3 + px2 + qx + 1 = (x - 1) Q(x) + R

x - 2 = 0, x = 2, R = 0,

4p + 2p = -9........(i)

x3 + px2 + 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