How do you find the polynomial function P of lowest degree, having rational coefficients, with the given zero: 3i?

${x}^{2} + 9$
If given zero is 3i, then -3i would also be a zero of the function, because complex zeros always occur in conjugate pairs. Thus the factors of the polynomial would be (x+3i)(x-3i) which equals ${x}^{2} + 9$