\(x^3-x^2-x+1=0\)
\(\Leftrightarrow\left(x^3-x^2\right)-\left(x-1\right)=0\)
\(\Leftrightarrow x^2\left(x-1\right)-\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x^2-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\mp1\end{matrix}\right.\)
\(\Rightarrow S=\left\{-1;1\right\}\)
