Answered: Let f(x) be an irreducible polynomial…

Let f(x) be an irreducible polynomial over a field F. Prove that thenumber of distinct zeros of f(x) in a splitting field divides deg f(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 8E: Let be an irreducible polynomial over a field . Prove that is irreducible over for all nonzero ...

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Let f(x) be an irreducible polynomial over a field F. Prove that the
number of distinct zeros of f(x) in a splitting field divides deg f(x).

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