Thanks- I had worked out that the degree of the splitting field is three, but what does this tell me? Since the polynomial is not separable,
Why do you think so?? Of course it is separable, and if you have any doubt just remember the basic theorem: any finite extension of a finite field (or any extension of a characteristic zero field) is separable. Furthermore, if you already knew the degree of the splitting field then, this being a prime, doesn't leave you many choices for the Galois group, does it? Tonio
presumably it's not the case that the size of the Galois group is 3. (But that 3 divides the size?) What automorphisms should I be trying?