Cryptography question:

3. (a) Show that the only irreducible polynomials in (Z/2Z)[x] of degree at most 2 are x, x + 1, and x2 + x +1. (b) Show that x4 +2+1 is irreducible in (Z/2Z)[x]. (Hint: If it factors, it must have at least one factor of degree at most 2.)