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Proposition 6.18 (Division Algorithm for Polynomials). Let n(x) be a polynomial that is not zero. For...

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Advance Math

Proposition 6.18 (Division Algorithm for Polynomials). Let n(x)be a polynomial that is not zero. For every polynomial m(x), thereexist polynomials q(x) and r(x) such that

m(x) = q(x)n(x) +r(x)

and either r(x) is zero or the degree of r(x) is smaller thanthe degree of n(x).

Prove

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