Chapter 4 - Polynomial and Rational Functions - 4.6 Complex Zeros; Fundamental Theorem of Algebra - 4.6 Assess Your Understanding - Page 241: 33

$2,3\pm 2i$ $f(x)=(x-2)(x-3+2i)(x-3-2i)$

Step 1. Use synthetic division to get a zero $x=2$ as shown in the figure. Step 2. Use the quotient and solve $x^2-6x+13=0$ to get $x=\frac{6\pm\sqrt {36-4(13)}}{2}=\frac{6\pm\sqrt {-16}}{2}=3\pm 2i$ Step 3. Thus $f(x)=(x-2)(x-3+2i)(x-3-2i)$