2.1.3 Factorisation

What is polynomial factorisation?

• Factorising a polynomial combines the factor theorem with the method of polynomial division
• The goal is to break down a polynomial as far as possible into a product of linear factors

How do I factorise a polynomial?

• At A level you will usually be asked to factorise a cubic – i.e. a polynomial where the highest power of x is 3

• To factorise a cubic polynomial f(x) follow the following steps:

• Step 1. Find a value p that makes f(p) = 0

• Step 2. Use polynomial division to divide f(x) by (x - p)

• Step 3. Use the result of your division to write

f(x) = (x - p) (ax² + bx + c)

• Step 4. If the quadratic (ax² + bx + c) is factorisable, factorise it and write f(x) as a product of three linear factors (if the quadratic is not factorisable, then your result from Step 3 is the final factorisation)