WAEC 2023 · Paper 1 · Q3

If $(x - 5)$ is a factor of $x^3 - 4x^2 - 11x + 30$ , find the remaining factors.

Worked solution (try it first)

Divide by $(x - 5)$ : $x^3 - 4x^2 - 11x + 30 = (x - 5)(x^2 + x - 6)$ .
Factorise the quadratic: two numbers that multiply to $-6$ and add to $1$ are $3$ and $-2$ , so $x^2 + x - 6 = (x + 3)(x - 2)$ .
The remaining factors are $(x + 3)$ and $(x - 2)$ , option C.