The factor theorem states that if \(f(a)=0\) when a polynomial \(f(x)\) is divided by \((x-a)\), then \((x-a)\) is a factor of \(f(x)\).

The factor theorem is useful for factorising cubic and quartic expressions.

Tip: Use your calculator to test different values of \(a\) to quickly determine whether \((x-a)\) is a factor of a polynomial \(f(x)\).