The factor theorem

The idea

If $f(a) = 0$, then $(x - a)$ is a factor of $f(x)$. Once you have one factor, divide (or compare coefficients) to get a quadratic, then factorise that.

1. Try small values such as $1, -1, 2, -2$ until $f(a) = 0$.
2. Divide $f(x)$ by $(x - a)$ to get a quadratic.
3. Factorise the quadratic to finish.

Watch out For a factor $(2x - 1)$, substitute $x = \frac{1}{2}$, not $x = 1$.