Assignment:
Q1. 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].
Q2. 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].
Provide complete and step by step solution for the question and show calculations and use formulas.