Answer
$x=1,\frac{-1\pm i\sqrt {3}}{2}$
$f(x)=(x-1)(x+\frac{1+ i\sqrt {3}}{2})(x+\frac{1- i\sqrt {3}}{2})$
Work Step by Step
Step 1. $x^3-1=0 \Longrightarrow (x-1)(x^2+x+1)=0 \Longrightarrow x=1\ and\ x=\frac{-1\pm\sqrt {1-4}}{2}=\frac{-1\pm i\sqrt {3}}{2}$
Step 2. We have $f(x)=(x-1)(x+\frac{1+ i\sqrt {3}}{2})(x+\frac{1- i\sqrt {3}}{2})$