$\begin{array}{l}
y = {x^3} - 3m{x^2} + 3\left( {m + 2} \right)x + m\\
y' = 3{x^2} - 6mx + 3\left( {m + 2} \right)\\
Hs\,dong\,bien\,tren\,R \Leftrightarrow y' \ge 0,\forall x \in R\\
\Leftrightarrow \left\{ \begin{array}{l}
a = 3 > 0\\
\Delta ' = 9{m^2} - 9\left( {m + 2} \right) \le 0
\end{array} \right. \Leftrightarrow 9{m^2} - 9m - 18 \le 0\\
\Leftrightarrow - 1 \le m \le 2\\
Do\,m \in Z\,nen\,m \in \left\{ { - 1;0;1;2} \right\} \Rightarrow co\,4\,gia\,tri.
\end{array}$
