If (x - 2) and (x + 1) are factors of the expression x³ + px² + qx + 1, what is the sum of p and q

-3

$\frac{17}{3}$

$\frac{2}{3}$

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

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