Answer
See table.
Work Step by Step
Step 1. Given $f(x)=3x^3+6x^2+x+7$, we can identify 0 sign changes indicating that there is 0 positive zeros. Put the numbers in the table.
Step 2. $f(-x)=-3x^3+6x^2-x+7$, we can identify 3 sign change indicating that there could be 3 or 1 negative zeros. Put the numbers in the table.
Step 3. There should be 3 total zeros. thus the number of nonreal zeros will be the remaining after taking real zeros into account. Complete the table as shown.