Let $\mathbb{F}_2$ be the finite field with two elements. Let $f(x) = x^6+x^4+x+1$ be in $\mathbb{F}_2[x]$. If $f(x)$ is irreducible, give a reason. If it is not irreducible, determine a factorization of $f$ into irreducible monic polynomials in $\mathbb{F}_2[x]$.
finite fields factorization
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finite-fields
factoring
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1What is *your* question? What have you tried? – 2011-12-13
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2@user21175: Welcome to Math.SE. For future reference, please known that it is polite to _ask_ a question rather than assign the community a problem. It is also good practice to specify any difficulties you have had with a problem, or to explain what you tried, and where you are stuck. – 2011-12-13
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1Never a bad idea to check whether this has a root in your ground field, and there are only two elements there to check. Is $1$ a root, for example? – 2011-12-13