Question

\(x^3-x^2-x+1=0\)

Answer 1

\(x^3-x^2-x+1=0\)

\(\Rightarrow x^2\left(x-1\right)-1\left(x-1\right)=0\)

\(\Rightarrow\left(x^2-1\right)\left(x-1\right)=0\)

\(\Leftrightarrow x=1\)

Answer 2

\(x^3-x^2-x+1=0\)

\(\Leftrightarrow x^2\left(x-1\right)-\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x^2-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-1\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left(x-1\right)^2\left(x+1\right)=0\)

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

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