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I am trying to prove that the polynomial $P = X^5 + X^2 + 1 ∈ F_2 [X]$ is irreducible.
What I did:
I showed that $X^2+X+1∈F_2[X]$ is the only irreducible polynomial of degree 2. Is there a way to use this to prove that $P$ is irreducible without checking all the polynomial products giving polynomials of degree $5$?