Define factor theorem.
Understand the Problem
The question is asking for a definition of the Factor Theorem, which is a fundamental concept in algebra and polynomial functions. It states that a polynomial f(x) has a factor (x - c) if and only if f(c) = 0, meaning that c is a root of the polynomial.
Answer
For a polynomial p(x), x-a is a factor if and only if p(a) = 0.
The Factor Theorem states that for a polynomial p(x), x-a is a factor of p(x) if and only if p(a) = 0.
Answer for screen readers
The Factor Theorem states that for a polynomial p(x), x-a is a factor of p(x) if and only if p(a) = 0.
More Information
The Factor Theorem connects the roots or zeros of a polynomial to its factors, aiding in polynomial factorization.
Tips
A common mistake is assuming p(a) = 0 implies x+a is a factor, rather it's x-a.
Sources
- Factor Theorem - Statement, Formula, Proof, Examples, Application - cuemath.com
- The Factor Theorem: What it says and how it works - Purplemath - purplemath.com
- Factor Theorem (Proof and Examples) - BYJU'S - byjus.com
AI-generated content may contain errors. Please verify critical information