Factorising Quadratic Expressions

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 42factors 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 15factors added
(1, 15)16
(3, 5)8
(-3, -5)-8
(-1, -15)-16

The factors are -3 and -5.