Taking Out Common Factors

Factorising is expansion in reverse: writing an expression as a product. The first tool is always the highest common factor (HCF).

Worked example 1. Factorise $6x + 9$.

HCF of 6 and 9 is 3: $6x + 9 = 3(2x + 3)$.

Worked example 2. Factorise $x^2 + 5x$.

Both terms contain $x$: $x^2 + 5x = x(x + 5)$.

Always check by expanding your answer — you must land back on the original expression: $3(2x+3) = 6x + 9$ ✓

The HCF can include letters: for $12x^2$ and $18x$, the HCF is $6x$, so $12x^2 + 18x = 6x(2x + 3)$.