JAMB 1983 · UME · Q5

If $x = 1$ is a root of the equation $x^3 - 2x^2 - 5x + 6 = 0$ , find the other roots.

Worked solution (try it first)

$x = 1$ is a root, so $x - 1$ is a factor.
Divide it out: $x^3 - 2x^2 - 5x + 6 = (x - 1)(x^2 - x - 6)$ .
Factorise the quadratic: two numbers that multiply to $-6$ and add to $-1$ are $-3$ and 2, so $x^2 - x - 6 = (x - 3)(x + 2)$ .
Each factor gives a root: $x = 3$ and $x = -2$ , option C.