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

For the expression x^2 + 6x + 8, the numbers in the brackets must multiply together to make 8 (the number at the end of the expression).

At the same time the numbers in the brackets must add together to make 6 (the number in front of the x).

So what two numbers, when multiplied together make 8; and when added together make 6?

what are the combination of factors that make the number value, and

which pair of factors also add up to the coefficient of the x term?

Negative signs have to be taken into account when determining the factors. remember that two negatives multiplied together give a positive result.

Factorising a quadratic is the opposite process to expanding aa binomial.

## Example 1

Factorise x^2 + 13x + 42

The numbers for the brackets multiply together to make 42; and add together to make 13:

 factors of 42 added 1 and 42 43 2 and 21 23 3 and 14 17 6 and 7 13 larr

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

## Example 2

Factorise a^2 - 8a + 15

The numbers for the brackets multiply together to make 15; and add together to make -8:

 factors of 15 added 1 and 15 16 3 and 5 8 -3 and -5 -8 larr -1 and -15 -16

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