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Factor Theorem (OCR AS Maths A): Revision Note

Exam code: H230

Roger B

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Roger B

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OCR Maths A: PureAQA Maths: PureEdexcel Maths: Pure

Factor theorem

What is the factor theorem?

  • The factor theorem is a very useful result about polynomials

  • A polynomial is an algebraic expression consisting of a finite number of terms, with non-negative integer indices only

2.5.3 Polynomial not polynomial, Edexcel A Level Maths: Pure revision notes

  • At A level you will most frequently use the factor theorem as a way to simplify the process of factorising polynomials

2.5.3 Factorised Polynomial Illustration, Edexcel A Level Maths: Pure revision notes

What do I need to know about the factor theorem?

  • For a polynomial f(x) the factor theorem states that:

    • If f(p) = 0, then (x - p) is a factor of f(x)

    AND

    • If (x - p) is a factor of f(x), then f(p) = 0

2.5.3 Factor Theorem Illustration, Edexcel A Level Maths: Pure revision notes

Examiner Tips and Tricks

  • In an exam, the values of p you need to find that make f(p) = 0 are going to be integers close to zero.

    • Try p = 1 and -1 first, then 2 and -2, then 3 and -3

    • It is very unlikely that you'll have to go beyond that. 

Worked Example

2.5.3 Factor Theorem Example, Edexcel A Level Maths: Pure revision notes
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Roger B

Author: Roger B

Expertise: Maths Content Creator

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.