How do you factorise a quadratic equation?
You should already be familiar with multiplying out brackets to arrive at a quadratic equation, which will look something like the following: (x + 2)(x + 3) = x2 + 2x + 3x + 6 = x2 + 5x + 6
Factorising is simply the reverse of this and, although it may look intimidating at first, the same simple method can be applied to every quadratic equation. This will be useful later on in your course, as it can be used to solve the equation to find x. Using the quadratic equation written above, we can see that 5x comes from adding 2x and 3x together, and 6 comes from multiplying the 2 and 3 in the brackets. So, if the question asked you to factorise x2 + 5x + 6, we are looking to create the expression (x + a)(x + b) where:
a + b = 5
a x b = 6
You can find a and b through simply testing different numbers and, with practice, you will be able to do this very quickly. In this case, we can deduce that a = 2 and b = 3. You can then fill in the brackets: (x + a)(x + b) = (x + 2)(x + 3) and you have successfully factorised the quadratic! If you are unsure if you have got the right answer, it is easy to check by simply multiplying out the brackets and checking if you arrive at the same quadratic equation that you started with.
