Factorising

Common factor

We factorise an expression by rewriting it as a product of factors. If we think back to removing brackets, the answer is now the question and the question is now the answer. We should ask ourselves; 'What was it before we removed the brackets?'

A great trick when factorising is to multiply out the brackets once you've got an answer and you should find that your answer matches with the question. If it doesn't, then you know you've done something wrong.

Try the example questions below.

Question

Factorise \(10 + 4x\)

The first thing we do is find the highest common factor (H.C.F) of \(10+4x\) and this will tell us the term that will go outside the bracket.

Factors of 10

Common factors are: -2, -1, 1 and 2.

Highest Common Factor (H.C.F.) of 10 and \(4x\) is 2.

\[10 + 4x = 2(... + ...)\]

To get the terms inside the bracket, we find \(2 \times ? = 10\) and then \( 2 \times ? = 4x\), namely 5 and \(2x\) respectively.

\[= 2(5 + 2x)\]

Remember you can multiply out your brackets now to check that your answer is correct.

Question

Factorise \(6a - 9\)

Highest Common Factor (H.C.F.) = 3.

\[6a - 9 = 3(2a - 3)\]

Question

Factorise \(15 + 10x\)

\[= 5(3 + 2x)\]

Question

Factorise \(3 - 12a\)

\[= 3(1 - 4a)\]

Question

Factorise \(20y - 6\)

\[= 2(10y - 3)\]