Factorising Quadratics: x ^2 ​​ − x = 12

Factorising a quadratic basing means 'putting it into 2 brackets'. The standard format for a quadratic equation is:ax^2 + bx + c = 0. You'll usually find that this becomes a lot easier when a=1. As well as factorising the quadratic you might be asked to solve it. This just means finding the values of x which make each bracket 0.So to begin, always start by rearranging into the standard format: x^2 - x - 12 = 0. Then write down the two brackets with the x's in : (x )(x ) = 0. Then find two numbers which multiply to give '-12' but also add/subtract to give '-1'. From a little trial and error we know that 3 and 4 add/subtract to give -1 and multiply to give 12. So we can now put 3 and 4 into the brackets and expand the brackets to check (x+3)(x-4)= x^2 - x -12. Congrats, we've now factorised it!Now to solve the equation, set each bracket equal to 0 and solve for x : (x+3) = 0 => x=-3 and (x-4)= 0 => x =4