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
\(\frac{2}{3}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #32431)