Let F be a field. Then the followingstatements are equivalent:(a) F is algebraically closed.(b) All irreducible polynomials in F[] are ofdegree 1.(c) If f(x) E F[x] is of degree > 1, then thereexist c, a1,..., an € F such that f(x) = c(x -a₁) ... (x − an).

(a) =) (b) Let f(x) be a irreducible polynomial in F[x].

Answered: F is algebraically closed.

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 3TFE

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