Let F be a field and f (x) e F[x] be a polynomial of degree > 1. Iff(a) = 0 for some a e F, then f (x) is reducible over F.%3D Let F be a field and f (x) e F[x] be a polynomial of degree > 1. Iff(a) = 0 for some a e F, then f (x) is reducible over F.%3D

Since α ∈ F, x- α ∈ F[x]. Also f(x) ∈ F[x].

Answered: Let F be a field and f(x) e F[x] be a…

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 be a field and f(x) e F[x] be a polynomial of degree > 1. If f(m =0 for some E F. thenf(x) is reducible over F.