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Question:

If $p{x}^3$ + $x^2$ + 3x + q is exactly divisible by (x + 2) and (x - 2), then the values of p and q are:

Explanation:

If f(x) is divisible by x - a, then f(a) = 0

f(x) = px³ + x² + 3x + q is divisible by x - 2, hence f(2) = 0
∴ 8p + 4 + 6 + q = 0
⇒ 8p + q = -10   ...(1)

f(x) = px³ + x² + 3x + q is divisible by x + 2, hence f(-2) = 0
∴ -8p + 4 - 6 + q = 0
⇒ -8p + q = 2   ...(2)

Solving (1) and (2), we get
q = -4 and p = -3/4

Hence, option (d).