Thread: Product of irreducible polynomials.

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

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

Originally Posted by tttcomrader

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

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

So far correct but $\displaystyle x^2+1 = (x+1)^2$.