# Factorising and D.O.T.S.

Factorising is just putting things in brackets…and it’s really cool *cough*

Simple Factorising

• Find the highest common factors of all terms
• If there are powers, find the highest powers in all terms
• Put these outside the brackets then fill in the brackets with what is needed to get the equation in the question
• Multiply out the brackets to check your answer

E.g. You can factorise 9x + 3 to get:

3(3x + 1)

E.g. You can factorise 6ab2 – 4ab to be:

2ab(3b – 2)

REMEMBER JUST FIND WHAT GOES INTO ALL THE TERMS AND PUT IT OUTSIDE THE BRACKETS

Factorising Quadratics

To factorise an expression such x2 + 5x + 6, you need to look for two numbers that add up to make 5 and multiply to give 6.

The only numbers that do this are 2 and 3 so this equation factorised is:

(x + 3)(x + 2)

Be careful of negatives….

If you had the equation x2 – 3x – 10 you need numbers that multiply to minus ten and add up to minus 3. The only numbers that do this are 2 and minus 5

So this factorised would be (x + 2)(x – 5)

The Difference Of Two SquaresWhen you have one thing squared minus another thing squared you can factorise it using this handy rule….and examiners LOVE to throw this in.

Always be on the look our for square numbers like 4,9,16,25,36 etc in an equation…there might be a D.O.T.S solution!

So x2 – 81 = x2 – 92 = (x + 9)(x – 9)

Always be on the look out for these…sometimes they will be a numerator or denominator in a fraction and this will help you simplify out the fraction (another examiner favourite).