Factor Theorem
Revision as of 13:38, 15 November 2007 by 10000th User (talk | contribs) (Found a proof I provided a long time ago, a gem hidden in the forums)
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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 .