Apply the Remainder Theorem

What you'll learn

1. State the Remainder Theorem: when p(x) is divided by (x - a), the remainder equals p(a)
2. Use the Remainder Theorem to evaluate a polynomial at a specific value without full substitution, by performing synthetic division
3. State and apply the Factor Theorem as a corollary: (x - a) is a factor of p(x) if and only if p(a) = 0
4. Test potential rational roots of a polynomial using the Factor Theorem
5. Explain why the Remainder Theorem is true using the polynomial division equation p(x) = (x - a)·q(x) + r

Prerequisites

• Perform polynomial operations