JAMB 2004 · UME · Q11

Find the values of $x$ where the curve $y = x^3 + 2x^2 - 5x - 6$ crosses the $x$ -axis.

Worked solution (try it first)

The curve crosses the $x$ -axis where $y = 0$ .
Try small numbers: $f(2) = 8 + 8 - 10 - 6 = 0$ , so $x - 2$ is a factor.
Divide out $x - 2$ : $x^3 + 2x^2 - 5x - 6 = (x - 2)(x^2 + 4x + 3)$ .
Factorise: $x^2 + 4x + 3 = (x + 1)(x + 3)$ , so the roots are $2, -1$ and $-3$ , option C.