Answer
The degree of the polynomial functino cannot be 3 as it has $4$ complex zeros.
Work Step by Step
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.
We have that $4\pm i$ and $(2+i)$ are zeros of $f(x)$, hence according to the Conjugate Pair Theorem $\overline{2+i}=2-i$ is also a zero of $f(x)$, hence $f(x)$ has at least 4 zeros, hence its degree cannot be 3.
