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).

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back