(a) Find a splitting field for the polynomial .

(b) Determine the Galois Group of over .

(c) Find all intermediate fields between and , by refering to the Fundamental Theorem of Galois Theory [FTG] to show you have them all.

I'm pretty sure that (a) is , (b) is (c) . I don't know how to justify (c) by using the Fundamental Theorem of Galois Theory. Also, I don't know how to determine the Galois Group for part (b). I know it is either or . But, I don't know how to show this.