Start with the field Z₂=({0,1}, + mod 2, mod 2). (1) Show that x³+x²+1 cannot be factored in a nontrivial way (into polynomials of degree less than 2 with coefficients in Z₃). (2) Let be the root of this polynomial. Construct a Galois field with 2³ = 8 elements. (3) Do the following computations: a) ², b) (1+)², c) (1+)³, d) ^-1.