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. $$$(x-3)(x-4) = x^2-7x+12$$$