I have a Group $\mathbb{Z_2}[x]/q$ where $q(x)=x^3+x+1$
In my textbook, there a multiplication table:
but I dont understand how the last $x+1$ comes. it should be
$(x^2+x+1)*(x^2+x+1) \quad mod \quad (x^3+x+1)$ right? I dont come to $x+1$ however, am I going the wrong way? this is my division:
