Identify the splitting field of x3 + x2 + 1 over Z2. Write the addition and Multiplication tables of the splitting field.
(x3 + x2 + 1) = (x - 1) (x2 - x - 1)
I know that (x2 - x - 1) does not have a root in Z3 so lets go to Z5.
Maybe (x2 - x - 1) = (x - 3) (x + 2) = (x + 2)2
I started the addition table but need some help finishing it.
0 1 u u2 u3 v v2 v3
0 0 1 u u2 u3 v v2 v3
1 1 0 u u 0 u2 u2 0 u3 u3 0 v v 0 v2 v2 0 v3 v3 0