Instructions for HW8:

Problem 2: Please use Galois theory here. (In one of early homeworks I assigned a problem that gave a different method.)

Problem 3: Please work through Example 4 on p. 563

Problem 17: Please note that the extension K/F need not be necessarily Galois. The same applies to Problem 18.

Polynomials (a) and (b): Try to pick the generators of the splitting fields and of the respective Galois groups as suitably as possible. This will simplify your computations. For (a), you may consult Problem 16 that was on HW 7. In either case write down the generators of the group and a complete list of equations.