Factor Theorem

Topic

Polynomials

Definition

The Factor Theorem states that a polynomial p(x) has a factor (x - r) if and only if p(r) = 0.

Description

The Factor Theorem is a powerful tool in polynomial algebra that bridges the concepts of roots and factors. This theorem provides a method for determining whether a given linear expression is a factor of a polynomial without performing long division. It's particularly useful in finding roots of polynomials and in polynomial factorization.

Understanding and applying the Factor Theorem is crucial for solving higher-degree polynomial equations and analyzing polynomial functions. It forms the basis for more advanced techniques in algebra and calculus, such as the Rational Root Theorem and methods for approximating roots. In practical applications, the Factor Theorem is used in various fields of science and engineering, particularly in situations involving polynomial modeling and analysis of complex systems.

For a complete collection of terms related to polynomials click on this link: Polynomials Collection