# Factorising Quadratic Expressions

GCSE(F), GCSE(H),

Factorising a quadratic expression, such as x2 + 6x + 8, means putting the brackets back in, to obtain an expression with two sets of brackets: (x + 4)(x + 2).

The answer will be in the form (x + a)(x + b), where a and b represent the missing numbers.

For the expression x2 + 8x + 12, the number 12 must be factors of 12 as ab = 12: possible factors are 1, 12 or 2, 6 or 3, 4.

The number 8 is obtained from adding the two x terms; a + b = 8.

So a and b are factors of 12 and add to 8. The pair of numbers that can do that are 6, 2.

x2 + 8x + 12 = (x + 6)(x + 2).

Negative signs have to be taken into account when determining the factors.

## Examples

1. Factorise x2 + 13x + 42.

Answer: (x + 6)(x + 7)

 factors of 42 factors added (1, 42) 43 (2, 21) 23 (3, 14) 17 (6, 7) 13

The factors are therefore 6 and 7.

2. Factorise a2 - 8a + 15.

Answer: (a - 3)(a - 5)

 factors of 15 factors added (1, 15) 16 (3, 5) 8 (-3, -5) -8 (-1, -15) -16

The factors are -3 and -5.