Chapter 4 - Polynomial and Rational Functions - 4.6 Complex Zeros; Fundamental Theorem of Algebra - 4.6 Assess Your Understanding - Page 241: 34

$-5,-4\pm i$ Step 3. Thus $f(x)=(x+5)(x+4-i)(x+4+i)$

Step 1. Use synthetic division to get a zero $x=-5$ as shown in the figure. Step 2. Use the quotient and solve $x^2+8x+17=0$ to get $x=\frac{-8\pm\sqrt {64-4(17)}}{2}=\frac{-8\pm\sqrt {-4}}{2}=-4\pm i$ Step 3. Thus $f(x)=(x+5)(x+4-i)(x+4+i)$