Answer
$$0$$
Work Step by Step
\begin{align*}
\lim _{x \rightarrow-\infty} \frac{x^{2}-4 x+8}{3 x^{3}}&=\lim _{x \rightarrow-\infty}\left(\frac{1}{3 x}-\frac{4}{3 x^{2}}+\frac{8}{3 x^{3}}\right)\\
&=0-0+0\\
&=0
\end{align*}
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