How would I show that $p(x)=x^5+x^2+1$ is an irreducible polynomial over $\Bbb Z_2=\{0,1\}$.
2026-04-05 02:59:20.1775357960
Irreducible Polynomials over Finite Fields
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Hints. It has no factors of degree one (why?). Then check whether your polynomial is divisible by the only irreducible polynomial of degree two over $\mathbb F_2$: $X^2+X+1$.