Answer
$x^4+13x^2+36$
Work Step by Step
The Complex Conjugate zeroes Theorem states that the conjugate of $i$ is also a zero of the polynomial $P(x)$.
Here, we have three zeroes of the polynomial $P(x)$ of degree $4$.
The factorization of $P(x)$ is given as follows:
$P(x)=(x-2i)(x+2i)(x-3i)(x+3i)$
Apply the difference square formula.
$P(x)=(x^2-(2i)^2(x^2-(3i)^2)=(x^2+4)(x^2+9)=x^4+9x^2+4x^2+36$
Hence, $P(x)=x^4+13x^2+36$