Factor Theorem
Revision as of 13:44, 15 November 2007 by 10000th User (talk | contribs)
This article is a stub. Help us out by expanding it. Template:Wikify This page is under heavy construction--10000th User 13:44, 15 November 2007 (EST)
Contents
[hide]Introduction
Theorem and Proof
Theorem: If is a polynomial, then is a factor iff .
- Proof: If is a factor of , then , where is a polynomial with . Then .
Now suppose that .
Apply division algorithm to get , where is a polynomial with and is the remainder polynomial such that .
This means that can be at most a constant polynomial.
Substitute and get .
But is a constant polynomial and so for all .
Therefore, , which shows that is a factor of .