How do you factorise a quadratic?

To factorise a quadratic, ax^2 + bx + c, we first want to ensure this is possible. We can do so by checking that the square root of b^2-4ac is not irrational. If this is the case, we can factorise the quadratic in a number of ways.

Either you can factorise intuitively e.g. x^2 + 7x + 12 = (x+3)(x+4) as 3+4=7 and 3*4=12 OR you can calculate the roots of the equation using the quadratic equation, and let the roots be called m and n. Then the quadratic equation may be factorised as a(x-m)(x-n).