JAMB 1983 · UME · Q10

If $x + 2$ and $x - 1$ are factors of the expression $lx^3 + 2kx^2 + 24$ , find the values of $l$ and $k$ .

Worked solution (try it first)

By the factor theorem, $x - 1$ is a factor, so the expression is 0 at $x = 1$ : $l + 2k + 24 = 0$ .
$x + 2$ is a factor, so it is 0 at $x = -2$ : $-8l + 8k + 24 = 0$ .
Divide by 8: $k = l - 3$ .
Put $k = l - 3$ into the first equation: $l + 2l - 6 + 24 = 0$ , so $3l = -18$ and $l = -6$ .
Then $k = -6 - 3 = -9$ , option A.