Polynomials and the Factor/Remainder Theorem

If $f(a) = 0$, then $(x-a)$ is a factor of $f(x)$.

When $f(x)$ is divided by $(x-a)$, the remainder is $f(a)$.

1. Test $f(1), f(-1), f(2), f(-2), ...$ to find a root.
2. Divide by the factor to get a quadratic.
3. Factorise the quadratic.

$f(x) = x^3 - 2x^2 - 5x + 6$.

$f(1) = 1 - 2 - 5 + 6 = 0$ ✓ → $(x-1)$ is a factor.

Divide: $x^3 - 2x^2 - 5x + 6 = (x-1)(x^2 - x - 6) = (x-1)(x-3)(x+2)$.