1. The problem statement, all variables and given/known data Construct a splitting s for the polynomial x^3+2x+1 over Z/Z3 2. Relevant equations 4=1 Mod 3 :P 3. The attempt at a solution So i'm actually quite confused. There are no roots for x+3+2x+1 over Z/Z3. I am used to constructing splitting fields with polynomials that have coefficients in a field of character zero, for example Q(i) is a splitting field of x+1 over Q. I guess i am confused because I don't know how to extensions of Z/Z3 will work, will the element I add not be reduced modulus 3? Will the new field have a new character? Any insight appreciated :-) Thanks PF!