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?

To factorise a quadratic:

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.