Answer
$5$
Work Step by Step
Step 1. Given $x=3$ as a zero, use synthetic division to find the quotient as $x^2-5x+1$, see figure.
Step 2. Solve $x^2-5x+1=0$ to get $x=\frac{5\pm\sqrt {25-4}}{2}=\frac{5\pm\sqrt {21}}{2}$
Step 3. Thus, the sum of the remaining zeros is $5$