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Let F be an infinite field and let f(x)∈ F[x]. If f(a) = 0 for infinitelymany elements a of F, show that f(x) = 0.

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 10E

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Let F be an infinite field and let f(x)∈ F[x]. If f(a) = 0 for infinitely
many elements a of F, show that f(x) = 0.

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