Prove that If f (x) is any polynomial of degree n 21 over a fieldF, then there exists an extension K of F such that f (x) has n roots in K and[K:F]

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Answered: If f (x) is any polynomial of degree…

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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If f (x) is any polynomial of degree n21 over a field F, then there exists an extension K of F such that f (x) has n roots in K and [K:F]