\(4.x^3-6x+10x-4=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^2-4x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x^2-4x+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=2\pm\sqrt{2}\end{matrix}\right.\)
\(5.2x^3-3x^2+x-6=0\)
\(\Leftrightarrow\left(x-2\right)\left(2x^2+x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\2x^2+x+3=0\left(\Delta=1-24=-23< 0\Rightarrow x\in\varnothing\right)\end{matrix}\right.\)
\(\Leftrightarrow x=2\)
\(6.x^3-6x^2+11x-6=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-5x+6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x^2-5x+6=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\\left(x-2\right)\left(x-3\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=3\end{matrix}\right.\)
