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Factorisation (CIE A Level Maths: Pure 3)
Revision Note
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
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)
Examiner Tip
- The method outlined above can be logically extended to factorise a polynomial of any degree.
Worked example
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