Remainder Theorem
Gr 12

The Grade 12 Remainder Theorem module introduces learners to a powerful algebraic tool used to evaluate polynomials efficiently and analyse their factors. This chapter strengthens symbolic manipulation skills and provides essential techniques for dealing with higher-degree polynomial expressions.

Learners begin by revising polynomial notation and substitution before exploring the Remainder Theorem, which states that the remainder when a polynomial f(x)f(x)f(x) is divided by (x−a)(x - a)(x−a) is simply f(a)f(a)f(a). The lessons cover applying the theorem to calculate remainders quickly, test potential factors, and verify solutions without performing long division. Students also learn the Factor Theorem as a direct extension, enabling them to determine whether a linear expression is a factor of a polynomial and to solve polynomial equations by finding their roots.

By the end of this module, learners will be able to apply the Remainder and Factor Theorems confidently, analyse polynomial expressions efficiently, and use these tools to solve equations and simplify algebraic problems—forming a key component of Grade 12 algebra and preparing students for advanced mathematics beyond school.