How do I factor for irreducible in F2[x]?

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I need to factor $x^7+x^6+x^2+x+1$ in $F_2[x]$. What are the steps?

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The hint.

  1. Think about roots of this polynomial;

  2. Prove that $x^2+x+1$ is an unique irreducible polynomial with degree two.

  3. Prove that $x^3+x^2+1$ and $x^3+x+1$ they are unique irreducible polynomials with degree three.