2.5.3 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