Factorisation (CIE A Level Maths: Pure 3)

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Polynomial 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

2.5.4 Product of linear factors, Edexcel A Level Maths: Pure revision notes

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

2.5.4 Cubic examples, Edexcel A Level Maths: Pure revision notes

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

2.5.4 Factorisation Illustration_qu, Edexcel A Level Maths: Pure revision notes

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

2.5.4 Factorisation Illustration_1, Edexcel A Level Maths: Pure revision notes

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

2.5.4 Factorisation Illustration_2, Edexcel A Level Maths: Pure revision notes

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

f(x) = (x - p) (ax2 + bx + c)

2.5.4 Factorisation Illustration_3, Edexcel A Level Maths: Pure revision notes

  • 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)2.5.4 Factorisation Illustration_4, Edexcel A Level Maths: Pure revision notes

Examiner Tip

  • The method outlined above can be logically extended to factorise a polynomial of any degree

Worked example

2.5.4 Factorisation Example, Edexcel A Level Maths: Pure revision notes

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Roger

Author: Roger

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.