## Precalculus (10th Edition)

The function has $5$ zeros so its degree is $5$, not $3$.
The Conjugate Pairs Theorem says that if a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. That is, if $a + bi$ is a zero then so is $a – bi$ and vice-versa. Since $2$, $i$ and $(3+i)$ are zeros of $f(x)$, then $\overline{i}=-i$ and $\overline{3+i}=3-i$ are also zeros of $f(x)$. Thus, $f(x)$ has $5$ zeros which means that its degree is $5$.