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(b) Show that f(x) = x4 + x + 1 is irreducible over Z2.

(c) Factor g(x) = x5 + x + 1 into a product of irreducible polynomials in Z2[x].

We have an irreducible polynomial if it cannot be factored into a product of polynomials of lower degree.

a)deg 1: x, x+1

deg 2: x^2+x+1

deg 3: x^3+x^2 + 1, x^3 + x +1

b) and c) get me confused.

I know a polynomial in F[x] is irreduble over F iff for all f(x),g(x) in F[x], p(x)|f(x)g(x) implies p(x)|f(x) or p(x)|g(x).

I don't know if that helps or if there is a simpler way to do this with degrees or something