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Irreducible polynomials

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a. Let F be a field and f (x) an irreducible polynomial of degree 3 in F [x]. Show that if K is an extension of F of dimension 10, then f(x) is irreducible in K[x].

b. Let F be a field and f(x) an irreducible polynomial of degree 5 in F[x]. Show that if K is an extension of F of dimension 7, then f(x) is irreducible in K[x].

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Irreducible polynomials are exemplified.

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a. Let F be a field and f(x) an ...

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