Topic Details (Notes format)

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.

Practice Questions

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