Chapter 4 - Polynomial and Rational Functions - 4.6 Complex Zeros; Fundamental Theorem of Algebra - 4.6 Assess Your Understanding - Page 241: 31

$1,\frac{-1\pm i\sqrt {3}}{2}$ $f(x)=(x-1)(x+\frac{1- i\sqrt {3}}{2})(x+\frac{1+ i\sqrt {3}}{2})$

Step 1. Factor the function $f(x)=x^3-1=(x-1)(x^2+x+1)$, thus one zero is $x=1$ Step 2. Solve $x^2+x+1=0$ to get $x=\frac{-1\pm\sqrt {1-4}}{2}=\frac{-1\pm i\sqrt {3}}{2}$ Step 3. Thus $f(x)=(x-1)(x+\frac{1- i\sqrt {3}}{2})(x+\frac{1+ i\sqrt {3}}{2})$