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# Methods of factorisation: inspection

When we factorise a quadratic expression, we need to put it "back into brackets".

If we want to factorise a quadratic expression $x^2+ax+b$, then we first look for a pair of numbers that multiply to give $b$, and add to give $a$.

We will try to factorise $x^2 - 7x +12$. We need numbers that multiply to give $12$, but that also add to give $-7$. This means that both the numbers we are looking for will be negative.

The pairs of negative numbers that multiply to give $12$ are $-1$ and $-12$, $-3$ and $-4$, and $-2$ and $-6$. The only pair that adds to give $-7$ is $-3$ and $-4$.

We now use these numbers to fill in the brackets. $$(x-3)(x-4) = x^2-7x+12$$