Edexcel A Level Maths: Pure:復習筆記2.5.3 Factor Theorem
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
Exam 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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