Answer
One of the missing zeros is $4+i$.
Work Step by Step
The Conjugate Pairs Theorem states that when a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. This means that, when $(p +i \ q)$ is a zero of a polynomial function with real number coefficients, then its conjugate $(p –i q)$, is also a zero of the function.
We see that the polynomial function has a degree of $4$, so it has $4$ zeros. $4+i$ is also a zero of the given function since $4-i$ is a zero (by the Conjugate Pairs Theorem). So, the missing fourth zero is $4+i$. The remaining zero must be real because if we had one more complex zero, it would require another complex zero (a new pair) and we would have more than 4 zeros total.
