we have the equation
[tex]f(x)=x^3-x^2-x+1[/tex]For x=1
f(x)=0
that means------> x=1 is a real root
Divide the given function by the factor (x-1)
x^3-x^2-x+1 : (x-1)
x^2-1
-x^3+x^2
-------------------
-x+1
x-1
---------
0
therefore
[tex]x^3-x^2-x+1=\left(x-1\right)\left(x^2-1\right)[/tex]Solve the quadratic equation
[tex]\begin{gathered} x^2-1=0 \\ x^2=1 \\ x=\pm1 \end{gathered}[/tex]therefore
