A third-degree polynomial $P(x)$, satisfies $P(0)= -3$ and $P(1)= 4$. When $P(x)$ is divided by $x^{2}+ x+ 1$, the remainder is $2x -1$. What is the quotient when $P(x)$ is divided by $x^2 + x + 1$?

Your answer seems reasonable.
Find out if you're right!