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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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    @HagenvonEitzen Yes, I realized that soon after, when I tried factoring it.2012-12-31

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You can't prove it because it's not true: $x^8+x+1 = (x^2+x+1)(x^6+x^5+x^3+x^2+1)$.

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    thanks. This problem is from my textbook on Abstract Algebra. I find that book has many errors.2012-12-31