Abstract algebra help--irreducible polynomials
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Abstract algebra help--irreducible polynomials

[From: ] [author: ] [Date: 11-06-28] [Hit: ]
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Find all irreducible polynomials of degree 3 in F_2[x].

Do I list all possible polynomials and then check them with some sort of formula??

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You have the right idea; just make sure they have no linear factors (which can be checked by making sure that 0 or 1 (mod 2) are not roots).

You should find that the only irreducible polynomials in F_2 [x] are
x^3 + x + 1 and x^3 + x^2 + 1.

I hope this helps!
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