Factorising Quadratics

One of the most important pieces of maths you`ll learn at GCSE and A Level is factorising a quadratic. Most methods taught by teachers are cumbersome and not intuitive at all - this custom method will half the time it takes you to solve a quadratic equation!

So, the method...

1. Get all the terms on one side, with the x^2 term positive. So if you have 24 - x^2 = 10x, take all the terms to the RIGHT hand side to make the x^2 positive:

24 - x^2 = 10x

0 = x^2 + 10x - 24

Then to make it look familiar, switch the sides:

x^2 + 10x - 24 = 0

2. Look at the SIGNS. These are exactly that - they are SIGNPOSTS to guide you to the right answer! The second sign is the most important:

If the second sign is a PLUS, both the signs in the answer have the same sign - and that sign is the first sign in the question.

If the second sign is a MINUS, the signs in the answer will have different signs - and we have to wait to see what they will be.

For for our example:

x^2 + 10x - 24 = 0

The second sign is a MINUS, so both the signs will be different in the answer:

(x + ?)(x - ?)

Conversely:

x^2 - 10x + 24 = 0

The second sign is a PLUS, so both the signs in the answer will have the sign of the first sign:

(x - ?)(x - ?)

3. For the rest of the method, you`ll have to get in touch with me for a lesson. But this is a good start!