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

Category: A-level課程, 國際課程, 教材筆記, 福利干貨 Date: 2022年10月25日 下午3:15

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

  • 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

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

 

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

2.5.3-Factor-Theorem-Example

 

 

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