Answer
$x^4 + 2 x^3 + 10 x^2 + 18 x + 9$
Work Step by Step
The factor theorem says that if $f(c)=0$, then $(x-c)$ is a factor of $f(x)$ and if $(x-c)$ is a factor of $f(x)$, then $f(c)=0$.
According to the Conjugate Pair Theorem, since $3i$ is a complex zero, then $-3i$ is also a complex zero.
We use the zeros to form factors and produce the function:
$P(x)=(x-(-1))^2(x-3i)(x-(-3i))=x^4 + 2 x^3 + 10 x^2 + 18 x + 9$
This indeed has a degree of $4$ and integer coefficients.
