Home » » If (x - 2) and (x + 1) are factors of the expression x3 + px2 + qx + 1, what is ...

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

### Question

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

### Options

A) 9

B) -3

C) 3

D) $$\frac{17}{3}$$

E) $$\frac{2}{3}$$

### Explanation:

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

## Dicussion (1)

• 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