How do you factorise a quadratic?

A quadratic equation is something that looks like this: ax²+bx+c. FACTORISING a quadratic means to put this equation in the form (dx+e)(fx+g). For example, take the equation x²+5x+6. The factorised form of this equation is (x+2)(x+3). How do we get here? First, let us look at the above example. Notice that 2+3=5, and 23=6. In this case, we found two numbers that add up to 5 and multiply to make 6. Now let's go through the steps for factorising quadratics. Let's use a new example, 6x²-x-2. 1. Look at the coeffient (number in front) of x². In our case, it is 6. We can factorise 6 in two ways: 61 and 32. Let's test 32 by writing some brackets like so: (3x  )(2x  ). 2. We need to find two numbers that multiply to give -2. Well, 1*-2=-2, so let's see if 1 and -2 work in our brackets. 3. We check if the numbers, 1 and -2, work by seeing whether 31+2-2=-1. Well, 31=3 and 2-2=-4, and adding these indeed gives -1. So we are done, and the final answer is: 6x²-x-2 = (3x-2)(2x+1).