Answer
$$-\infty $$
Work Step by Step
\begin{align*}
\lim _{x \rightarrow -\infty}\frac{2x^5+3x^4-31x}{8 x^4-31x^2+12}&= \lim _{x \rightarrow -\infty}\frac{x^5}{x^4}\frac{2 +3x^{-1}-31x^{-4}}{8 -31x^{-2}+12x^{-4}}\\
&=\lim _{x \rightarrow -\infty}\frac{x^5}{x^4}\lim _{x \rightarrow -\infty}\frac{2 +3x^{-1}-31x^{-4}}{8 -31x^{-2}+12x^{-4}}\\
&=\frac{2}{8}\lim _{x \rightarrow -\infty} x \\
&=-\infty.
\end{align*}
