Answered: Suppose that D is an integral domain…

Suppose that D is an integral domain and F is a field containing D.If f(x) ∈ D[x] and f(x) is irreducible over F but reducible over D,what can you say about the factorization of f(x) over D?

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 17E: Suppose that f(x),g(x), and h(x) are polynomials over the field F, each of which has positive...

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Question

Suppose that D is an integral domain and F is a field containing D.
If f(x) ∈ D[x] and f(x) is irreducible over F but reducible over D,
what can you say about the factorization of f(x) over D?

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