Dividing and factorising polynomial expressionsFactor theorem

A polynomial is an algebraic expression involving many terms and can be factorised using long division or synthetic division.

Part ofMathsAlgebraic and trigonometric skills

Factor theorem

Factorising and solving

Often, factorising a polynomial requires some trial and error. Remember that, if an expression is a factor, when you divide the polynomial by it, the remainder \(= 0\).

To put it another way, \(f(x) = 0\).

So, if \((x - a)\) is a factor, \(f(a) = 0\).

To find the answer, you need to try dividing the polynomial by simple factors to see which one gives a remainder of zero.