Chapter 3 - Polynomial and Rational Functions - Section 3.3 Complex Zeros; Fundamental Theorem of Algebra - 3.3 Assess Your Understanding - Page 231: 34

$-5,-4\pm i$ $f(x)=(x+5)(x+4+i)(x+4-i)$

Step 1. Use synthetic division (as shown in the figure) to find zero(s) of $f(x)=x^3+13x^2+57x+85$ as $x=-5$. Step 2. Use the quotient to find other zeros $x^2+8x+17=0 \Longrightarrow x=\frac{-8\pm\sqrt {64-4(17)}}{2}=-4\pm i$ Step 3. We have $f(x)=(x+5)(x+4+i)(x+4-i)$