Let f (x) and g(x) be irreducible polynomials over a field
Chapter 21, Problem 32E(choose chapter or problem)
Problem 32E
Let f (x) and g(x) be irreducible polynomials over a field F and let a and b belong to some extension E of F. If a is a zero of f (x) and b is a zero of g(x), show that f (x) is irreducible over F(b) if and only if g(x) is irreducible over F(a).
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