1. Let F be a field and let f(x), g(x), n(x). k(x), and h(x) bepolynomials in F[x]. Prove that if f(x) = g(x)(mod n(x))and h(x) = k(x)(mod n(x)) where degree of n(x) > 0, thenf(x) + h(x) = (g(x) + k(x))(mod n(x)).Proof/

Given thatLet F be a field and let f(x) , g(x) , n(x) , k(x) , and h(x) be polynomials in F[x] .We…

Answered: Let F be a field and let f(x), g(x),…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 16E

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Let F be a field and let f(x), g(x), n(x). k(x), and h(x) be polynomials in F[x]. Prove that if f(x) = g(x)(mod n(x)) and h(x) = k(x)(mod n(x)) where degree of n(x) > 0, then f(x) + h(x) = (g(x) + k(x))(mod n(x)).