How do we factorise?

The general form of factorising is that if we have ab+ac, we can rewrite this as a(b+c). We multiply each statement inside the bracket by a. So we’re effectively ripping out common terms. We are dividing b and c by a and then placing a on the outside. An example is 2x+4x²=0. This is a quadratic, so we can either use the quadratic formula to solve, or we can factorise by noticing that ‘2x’ goes both into 2x (2x/2x=1) and 4x² (4x²/2x=2x). So we find that 2x(1+2x)=0. Then we have to make 2x=0 and (1+2x)=0, so x=0 and -1/2.