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# Bezout's Theorem for Polynomials

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Suppose that a(x) and m(x) are relatively prime polynomials in F[x]. Bézout's Theorem guarantees the existence of polynomials u(x) and v(x) in F[x] such that...
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https://brainmass.com/math/number-theory/bezouts-theorem-polynomials-47225

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Question

Suppose that a(x) and m(x) are relatively prime polynomials in F[x]. Bézout's Theorem guarantees the existence of polynomials u(x) and v(x) in F[x] such that

a(x)u(x) + m(x)v(x) = 1.

Given this, prove that there exist polynomials r(x) and s(x) in F[x] such that the degree ...

#### Solution Summary

This is a proof of the division theorem that uses Bezout's Theorem for Polynomials.

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