Sorry if this is a really dumb question but
I am trying to figure out what the ring $\mathbb{Z}[x]/(3x+3)$ is.
I know that $\mathbb{Z}[x]/(x+1) = \mathbb{Z}$, you can just set $x=-1$ to reduce all the polynomials in $\mathbb{Z}[x]$ to constants in order to see this. But I guess you can't do a similar thing with $3x+3$ because $3$ is not invertible in $\mathbb{Z}$ and so you can't "solve for $x$" in the equation $3x+3=0$. So how do you figure out what this ring is? (I'm guessing it's not $\mathbb{Z}$.) I also know that $3x+3$ is reducible, but I'm not exactly sure how that makes a difference. Thanks for any help.
PS This is not a homework question. I am just curious.
