Chapter 3 - Polynomial and Rational Functions - Section 3.3 Complex Zeros; Fundamental Theorem of Algebra - 3.3 Assess Your Understanding - Page 231: 26

$-3i,-2,\frac{1}{3}$.

Step 1. As $x=3i$ is a zero, we have $x=-3i$ also a zero and $(x-3i)(x+3i)=x^2+9$ is a factor of the function. Step 2. Use synthetic division (two steps) or long division (as shown in the figure) to get the quotient. Step 3. Find other zeros $3x^2+5x-2=0 \Longrightarrow (3x-1)(x+2)=0 \Longrightarrow x=-2,\frac{1}{3}$.