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Factor Theorem (OCR AS Maths: Pure)
Revision Note
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
- At A level you will most frequently use the factor theorem as a way to simplify the process of factorising polynomials
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
Examiner Tip
- 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
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