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Theorem (Division Algorithm For Polynomials)

Let $F$ be a field and let $f(x)$ and $g(x)\in F[x]$ with $g(x)\neq 0$. Then there exist unique polynomials $q(x)$ and $r(x)$ such that $f(x)=g(x)q(x)+r(x)$ and either $r(x)=0$ or $\deg r(x) < \deg g(x)$.

The following pages link to this page.

Problem.DivisionAlgorithmForPolynomialsProof
Schedule.20140129
Schedule.20140131
Schedule.20170201
Schedule.20170203
Schedule.20170208
Schedule.AllProblems442
Theorem.DivisionAlgorithmForPolynomials

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Page last modified on January 27, 2014, at 12:42 PM

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HomePage Current Problems All Problems Pictures ProblemsByWeek List of Problems List of Definitions List of Theorems List of Conjectures All Recent changes (use this to find a page that may have been lost)	Theorem Division Algorithm For Polynomials Please Login to access more options. Theorem (Division Algorithm For Polynomials) Let $F$ be a field and let $f(x)$ and $g(x)\in F[x]$ with $g(x)\neq 0$. Then there exist unique polynomials $q(x)$ and $r(x)$ such that $f(x)=g(x)q(x)+r(x)$ and either $r(x)=0$ or $\deg r(x) < \deg g(x)$. The following pages link to this page. Problem.DivisionAlgorithmForPolynomialsProof Schedule.20140129 Schedule.20140131 Schedule.20170201 Schedule.20170203 Schedule.20170208 Schedule.AllProblems442 Theorem.DivisionAlgorithmForPolynomials Edit Page History Source Attach File Backlinks List Group Page last modified on January 27, 2014, at 12:42 PM
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