# Math Help - Product of irreducible polynomials.

1. ## Product of irreducible polynomials.

Let $f(x)=x^3+x^2+x+1 \in Z_{2}[x]$. Write f(x) as a product of irreducible polynomials over $Z_{2}$

I have $f(x)=(x^2+1)(x+1)$, they both have zeros in $Z_{2}$, is that right?

2. Originally Posted by tttcomrader
Let $f(x)=x^3+x^2+x+1 \in Z_{2}[x]$. Write f(x) as a product of irreducible polynomials over $Z_{2}$

I have $f(x)=(x^2+1)(x+1)$, they both have zeros in $Z_{2}$, is that right?
So far correct but $x^2+1 = (x+1)^2$.