Factorising Quadratics: Non-Monic

In this video we’re going to discover how to factorise quadratics that don’t have 1 as the coefficient of the x-squared term. These are called non-monic quadratics. We can do it by trial and error and just spotting the factors, but this takes a lot of trial an error. Luckily there is a different method we can use instead, which we will looks at in this video. Start by multiplying the number in front of the x-squared by the coefficient on it’s own. List out the factors of this multiplication. Which pair of factors add to give the number in front of the x term in the question? Rewrite the question with these two numbers, so it has the x-squared term, two different x-terms and a single coefficient. Now split this four term quadratic into two parts - the first two terms and the second two terms are grouped together. Now factorise each part. You should end up with two identical brackets. If they aren’t identical, go back and check you haven’t made any mistakes so far. The first bracket is the identical bracket you already have, and the second bracket are the two outside terms. This method will work for any non-monic quadratic, and saves a lot of time! As always in Maths, we should then go back and check our answer by quickly expanding the brackets to make sure we’re correct. We will look at how to solve quadratics in another video.