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Math Help - Irreducible Polynomials

  1. #1
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    Irreducible Polynomials

    Could somebody please give me some help on this subject.
    I thought in Z2[x] the polynomial x5+x4+1 can be factored as (x3+x+1)(x2+x+1)?
    I am confused as the user JavaMan on this website abstract algebra - Find all irreducible monic polynomials in $\mathbb{Z}/(2)[x]$ with degree equal or less than 5 - Mathematics Stack Exchange lists x5+x4+1 as a irreducible polynomial, and expands (x3+x+1)(x2+x+1) to x5+x4+x2+x+1.
    I am doing this correctly? If not please explain what I am doing wrong.
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  2. #2
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    Re: Irreducible Polynomials

    Solution :

    Given x^5+x^4+1=0
    the factor of the equation (x^3-x+1)(x^2+x+1)=0
    again if you multiply it you will get the same equation
    x^5+x^4+1=0
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