Suppose that f (x) and g(x) are irreducible over F and that deg f (x) and deg g(x) are relatively prime. If a is a zero of f (x) in some extension of F, show that g(x) is irreducible over F(a).

# Suppose that f (x) and g(x) are irreducible over F and

## Solution for problem 6E Chapter 21

Contemporary Abstract Algebra | 8th Edition

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Contemporary Abstract Algebra | 8th Edition

Get Full SolutionsSince the solution to 6E from 21 chapter was answered, more than 232 students have viewed the full step-by-step answer. Contemporary Abstract Algebra was written by and is associated to the ISBN: 9781133599708. The full step-by-step solution to problem: 6E from chapter: 21 was answered by , our top Math solution expert on 07/25/17, 05:55AM. The answer to “Suppose that f (x) and g(x) are irreducible over F and that deg f (x) and deg g(x) are relatively prime. If a is a zero of f (x) in some extension of F, show that g(x) is irreducible over F(a).” is broken down into a number of easy to follow steps, and 41 words. This textbook survival guide was created for the textbook: Contemporary Abstract Algebra , edition: 8. This full solution covers the following key subjects: deg, irreducible, relatively, prime, extension. This expansive textbook survival guide covers 34 chapters, and 2038 solutions.

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Suppose that f (x) and g(x) are irreducible over F and