How to Use Remainder Theorems (Polynomial Division) Definition, Types, Examples & Uses

How to Use Remainder Theorems (Polynomial Division)

Subject: Mathematics

Book: Maths Mastery

The Remainder Theorem states that the remainder when a polynomial f(x) is divided by (x – a) is simply f(a). For example, if you want the remainder when x² – 5x + 6 is divided by (x – 3), evaluate f(3) = 3² – 5×3 + 6 = 9 – 15 + 6 = 0. The Factor Theorem extends this, indicating if f(a) = 0, then (x – a) is a factor of the polynomial. These shortcuts alleviate long division and facilitate polynomial factoring, essential in solving polynomial equations, analyzing algebraic structures, and simplifying advanced math problems with speed and precision.