## Precalculus (10th Edition)

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. Thus if $-3+5i$ is a zero, $-3-5i$ must also be a zero, but here it isn't. Also, the degree is $4$, hence it can at most have $4$ zeros by the fundamental theorem of algebra, which are given, hence $-3-5i$ cannot be another zero, thus it is false.