9. (16 points) Given the function
$$
f(x)=3 \lg (x+2)-\log _{2} x,
$$

the set $M=\left\{n \in \mathbf{Z} \mid f\left(n^{3}-3 n^{2}-10 n+32\right) \geqslant 0\right\}$. Find $M$.
9. It is easy to know from differentiation that the function $f(x)$ is monotonically decreasing,
$$
\begin{array}{l}
f(8)=0 . \\
\text { Then } 00 . \\
\text { Also, } g(3)=2>0 \text {, so } M=\{-3,2,3,4\} .
\end{array}
$$