Factorise: GCSE Maths Definition

Written by: Jamie Wood

Reviewed by: Dan Finlay

Published

22 November 2024

Read time

2 minutes

Contents

What does factorise mean?

In GCSE maths you may be asked to factorise an algebraic expression. This means writing the expression as a product (multiplication) of two or more factors. For example, writing $12 x + 18$ as $6 (2 x + 3)$ , or writing $x^{2} - 2 x - 8$ as $(x + 2) (x - 4)$ .

What different types of factorising are there?

Factorising two or more terms with a common factor is usually straightforward, e.g. $5 x + 15$ can be written as $5 (x + 3)$ as the common factor is $5$ . Longer expressions work in the same way, e.g. $4 x^{2} + 4 x + 4$ can be rewritten as $4 (x^{2} + x + 1)$ .

Factorising by grouping involves using a common bracket as the common factor. E.g. $3 x (t + 4) + 2 (t + 4)$ can be factorised to $(3 x + 2) (t + 4)$ .

Factorising quadratics involves rewriting an expression of the form $a x^{2} + b x + c$ . For example, rewriting $x^{2} - 4 x - 21$ as $(x + 3) (x - 7)$ or rewriting $6 x^{2} - 7 x - 3$ as $(3 x + 1) (2 x - 3)$ .

You can find out more about factorising in our revision notes on factorising, and factorising quadratics for GCSE maths.

What does fully factorise mean?

GCSE maths questions will often ask you to fully factorise an expression. This means using the highest common factor, rather than just any factor.

For example, $24 x + 12$ can be factorised to $3 (8 x + 4)$ , however 3 is not the highest common factor. The highest common factor is 12, so this expression fully factorised would be $12 (2 x + 1)$ .

What is the opposite of factorising?

The opposite of factorising is expanding. This is very useful for your GCSE maths exam as it can be used to check your factorisation.

E.g. If you are asked to factorise $6 x^{2} - 7 x - 3$ , and you find the answer to be $(3 x + 1) (2 x - 3)$ , you can expand the brackets and check that the result is $6 x^{2} - 7 x - 3$ .

What is factorising used for?

As well as writing expressions more simply, factorising is a useful step when rearranging formulae and solving equations. You can read more about this in our revision notes about rearranging formulae and solving quadratic equations. It is also quite useful when dealing with algebraic fractions.

Factorising revision resources to ace your exams

Learn more about factorising and factorising quadratics with our revision notes. To test your knowledge, try our factorising exam questions.

For quick-fire GCSE maths revision use our collection of interactive flashcards for GCSE maths. We also have past papers for your exam practice.

Explore GCSE maths revision resources

Sign up for articles sent directly to your inbox

Receive news, articles and guides directly from our team of experts.

Share this article