Determine the degree [K:F] of the extension K over F, where K is a splitting field for the given polynomial:

i) $\displaystyle F = Z_2, x^7 -1$

ii) $\displaystyle F = Z_2, x^7 -1$

I can do these type of problems for the case F=Q, but how do you go about it with a finite field such as Z_2?