Quadratic equations

Multiply these brackets to remind yourself how to factorise.

• ( x + 2 ) ( x + 5 ) = x² + 7x + 10
• ( x + 2 ) ( x + 3 ) = x² + 5x + 6
• ( x - 3 ) ( x - 5 ) = x ² - 8x + 15
• ( x + 6 ) ( x - 5 ) = x² + x - 30
• ( x - 6 ) ( x + 5 ) = x² - x - 30

To factorise an expression such x² + 5x + 6, you need to look for two numbers that add up to make 5 and multiply to give 6.

The factor pairs of 6 are:

• 1 and 6
• 2 and 3

2 and 3 add up to 5. So: (x +2) (x+3) = x² + 5x + 6

Factorising expressions gets trickier with negative numbers.

Some quadratic expressions have only a term in x² and a number such as x² - 25.

These quadratic expressions have no x term.

Using our method to factorise quadratics means we look for two numbers that multiply to make -25 and add to make 0.

The only factor pair that will work are 5 and -5. So:

(x + 5)(x – 5) = x² - 25

Not all quadratic expressions without an x term can be factorised.