Solution
= Solution
In the <quotient ring>, the classes of $x-1$ and $x^2+x+1$ are nonzero: neither nonzero polynomial of degree less than three belongs to the ideal generated by $x^3-1$. But their product is the zero class, since
$$
(x-1)(x^2+x+1)=x^3-1.
$$
The quotient thus contains <zero divisors>, so \b[it is not an integral domain].