Step 1
\(x^{3}-3x^{2}+4x-2=0\)
Step 2
\(x-1| \frac{x^{2}-2x+2}{x^{3}-3x^{2}+4x-2} \frac{x^{3}-x^{2}}{-2x^{2}+4x-2}|\frac{-2x^{2}+2x}{2x-2}|(2x-2)\)
Step 3
\(x-1|\frac{x^{2}-2x+2}{x-1}(x^{2}-2x+2)=0\)

\(x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\)

\(x=\frac{-(-2)\pm \sqrt{(-2)^{2}-4(1)(2)}}{2(1)}\)

\(x = 1.1 \pm i\)

\(f(x) = (x-(1+i)) (x-(1-i)) (x-1)\)

\(x=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\)

\(x=\frac{-(-2)\pm \sqrt{(-2)^{2}-4(1)(2)}}{2(1)}\)

\(x = 1.1 \pm i\)

\(f(x) = (x-(1+i)) (x-(1-i)) (x-1)\)