division of polynomials in rings

Hey,

I don't know how to do the following question:

For which integers $\displaystyle n$ does $\displaystyle x^2+x+1$ divide $\displaystyle x^4+3x^3+x^2+6x+10$ in $\displaystyle \mathbb{Z}/n\mathbb{Z}[x]$?

I'm afraid I'm not entirely sure what to do for this question. I think my confusion for this question begins with the definition of $\displaystyle \mathbb{Z}[x]$. Is $\displaystyle \mathbb{Z}[x]$ the ring of algebraic integers? Should I be looking an integer $\displaystyle x$ that makes the 2 above polynomials equal to 0, then find out what integer multiples make the 2 polynomials equal to 0 as well?

Thanks for your time.