Chapter 27.4
Remainder theorem
What You'll Learn
Understand the Remainder Theorem and its connection to polynomial division
Apply the theorem to find remainders without performing full division
Use P(a) to find the remainder when dividing by (x - a)
Extend the theorem to divisors of the form (ax - b) using P(b/a)
Verify that synthetic division and the Remainder Theorem yield identical results
What You'll Practice
1
Finding remainders using the Remainder Theorem for divisors like (2x - 5)
2
Comparing synthetic division results with Remainder Theorem calculations
3
Solving for unknown coefficients using given remainder conditions
4
Working with polynomials containing multiple variables and missing terms
Why This Matters
The Remainder Theorem gives you a powerful shortcut for polynomial division that saves time on tests and homework. Instead of lengthy synthetic or long division, you simply plug in a value and evaluatea skill essential for factoring, graphing, and advanced algebra topics.
Before You Start — Make Sure You Can:
This Unit Includes
4 Video lessons
Practice exercises
Skills
Remainder Theorem
Polynomials
Synthetic Division
Polynomial Division
Evaluation
Systems of Equations
