More than one common factor

For some expressions, a combination of letters and numbers will make up the highest common factor.

Factorise \(\text{4x}^{2} + \text{2x}\)

It can be helpful to look at the numbers and the letters separately.

The HCF of 4 and 2 is 2.

The HCF of \(\text{x}^{2}\) and \(\text{x}\) is \(\text{x}\).

So the highest common factor of \(\text{4x}^{2}\) and \(\text{2x}\) must be \(\text{2x}\).

\(\text{4x}^{2} ÷ \text{2x = 2x}\)

\(\text{2x} ÷ \text{2x = 1}\)

This gives \(\text{2x(2x + 1)}\)

Factorise \(\text{6a}^{2} - \text{9a}^{3}\)

The HCF of 6 and 9 is 3.

The HCF of \(\text{a}^{2}\) and \(\text{a}^{3}\) is \(\text{a}^{2}\).

So the highest common factor of \(\text{6a}^{2}\) and \(\text{9a}^{3}\) is \(\text{3a}^{2}\).

\(\text{6a}^{2} ÷ \text{3a}^{2} = \text{2}\)

\(\text{9a}^{3} ÷ \text{3a}^{2} = \text{3a}\)

This gives \(\text{3a}^{2} \text{(2 - 3a)}\)

Question

Factorise \({16c^2} - {24c}\)