4.3.1 The Remainder Theorem

Question 1

remainder theorem

Answer 1

• If a polynomial p (x) is divided by (x – c), then its remainder is p (c).
  Note in (x – c), the c is subtracting; as a result, any constant must change its sign before being substituted into the polynomial.
  • This theorem and synthetic division allow the evaluation of some really big and complicated polynomials that might
  otherwise just baffle everybody.
  • The remainder will always have less value than the dividing expression.
  • The remainder will not have any x-terms, or you would be able to continue dividing.