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How to prove that $$x^{2^n}+x+1$$ is irreducible in $F_2$

-Is this question relevant to finite field?

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    @CalvinLin It might still be the product of two smaller degree polynomials (which also have no roots in $\mathbb F_2$).2012-12-31
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    You might be interested in this http://math.stackexchange.com/questions/122274/why-xpn-x1-is-irreducible-in-mathbbf-p-only-when-n-1-or-n-p-22012-12-31
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    @HagenvonEitzen Yes, I realized that soon after, when I tried factoring it.2012-12-31

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