\(x^3-2x^2+2x=0\)
\(\Rightarrow x\left(x^2-2x+2\right)=0\)
\(\Rightarrow x\left(x^2-2.x.1+1^2+1\right)=0\)
\(\Rightarrow x\left[\left(x-1\right)^2+1\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\\left(x-1\right)^2+1=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\\left(x-1\right)^2=-1\end{matrix}\right.\Rightarrow x=0\)
\(2x^3-5x^2+8x-5=0\)
\(\Rightarrow2x^3-3x^2-2x^2+5x+3x-5=0\)
\(\Rightarrow\left(2x^3-2x^2\right)-\left(3x^2-3x\right)+\left(5x-5\right)=0\)
\(\Rightarrow2x^2\left(x-1\right)-3x\left(x-1\right)+5\left(x-1\right)=0\)
\(\Rightarrow\left(x-1\right)\left(2x^2-3x+5\right)\)
