\(\left(x-2\right)^2\left(x+1\right)\left(x-4\right)< 0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x+1\right)\left(x-4\right)< 0\\\left(x-2\right)^2\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-1< x< 4\\x\ne2\end{matrix}\right.\)
\(\left(x-2\right)^2\cdot\left(x+1\right)\cdot\left(x-4\right)< 0\)
\(\Rightarrow\left[{}\begin{matrix}\left(x-2\right)^2< 0\left(\text{không thỏa mãn }\left(x-2\right)^2\ge0\right)\\x+1< 0\\x-4< 0\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x+1< 0\\x-4< 0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x< -1\\x< 4\end{matrix}\right.\)
Nếu x < -1 thì \(\left(x-2\right)^2\cdot\left(x+1\right)\cdot\left(x-4\right)>0\left(\text{trái với giả thiết đề bài}\right)\\ \Rightarrow x< -1\text{ không thỏa mãn}\)
Vậy x < 4
