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Let F be a field and let f(x) be an element of F[x] be an an...

Let F be a field and let f(x) be an element of F[x] be an an irreducible polynomial. Suppose K is an extension field containing F and that alpha is a root of f(x). Define a function f: F[x] ---> K by f:g(x) = g(alpha). Prove the ker(f) =<f(x)>.

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