Answer
Not correct factorization
Correct: $(x-1)(x^2+x+1)$
Work Step by Step
We graph the polynomial functions:
$$\begin{align*}
p_1(x)&=x^3-1\\
p_2(x)&=(x-1)(x^2-x+1).
\end{align*}$$
Because the two graphs do not coincide, this means that the polynomial $p_1(x)=x^3-1$ was not factored correctly.
Factor the polynomial $p_1(x)$ correctly:
$$\begin{align*}
p_1(x)&=x^3-1=(x-1)(x^2+x+1).
\end{align*}$$
We draw $p_2(x)=(x-1)(x^2+x+1)$ and notice that now the two graphs coincide.