Factorising by finding a common factor

To an expression, rewrite it as a product of factors.

This is the opposite process to removing brackets:

a removing brackets answer is the same as a factorising question
a removing brackets question is the same as a factorising answer

We could ask the question, 'What was it before the brackets were removed?'

Example

Factorise \(10 + 4x\)

The first thing to do is find the highest common factor (H.C.F) of \(10\) and \(4x\).

This will tell us the term that will go outside the bracket.

The Highest Common Factor (H.C.F.) = 2.

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

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

This is \(5\) and \(2x\) respectively:

So \(10+4x=2(5+2x)\)

Remember to multiply out the brackets now to check that the answer is correct.

Now try the example questions below.

Question

Factorise \(6a - 9\)

Question

Factorise \(15 + 10x\)

Question

Factorise \(x^{2}+5x\)

Question

Factorise \(3{a^2} - 12a\)

Question

Factorise \(20xy - 6x\)

Question

Factorise \(20{y^2} - 5y\)

Factorising an algebraic expressionFactorising by finding a common factor