Thread: Irreducible Polynomials

1. 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.

2. 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