JAMB 1995 · UME · Q11

If $x - 1$ and $x + 1$ are both factors of $x^3 + px^2 + qx + 6$ , evaluate $p$ and $q$ .

Worked solution (try it first)

By the factor theorem, the expression is 0 at $x = 1$ : $1 + p + q + 6 = 0$ , so $p + q = -7$ .
It is 0 at $x = -1$ : $-1 + p - q + 6 = 0$ , so $p - q = -5$ .
Add the equations: $2p = -12$ , so $p = -6$ and $q = -1$ , option A.