Solve

http://www.d.umn.edu/~jgallian/TF 1. Show that x50 - 1 has no multiple zeros in any extension of Z3. 2. Suppose that p(x) is a quadratic polynomial with rational coeffi- cients and is irreducible over Q. Show that p(x) has two zeros in Q[x]/

+x + 1 = (x + x+ 1). (x + x + 1) over Zz? 15. Show that a finite extension of a finite field is a simple extension. 16. Let R be an integral domain that contains a field F as a subring. If R is finite dimensional when viewed as a vector space over F, prove that R is a field