Find all the zeros. Write the answer in exact form. \[ g(x)=x^{3}-5 x^{2}+12 x+18 \] If there is more than one answer, separate them with commas. Select "None" if applicable. The zeros of \( g(x): \)

To find the zeros of the polynomial \( g(x) = x^{3} - 5x^{2} + 12x + 18 \), we can use the Rational Root Theorem. Testing possible rational roots, we find that \( x = -2 \) is a root. Using synthetic division, we can then factor the polynomial into \( (x + 2)(x^{2} - 7x + 9) \). Next, we solve the quadratic equation using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), leading us to the two remaining roots: \( x = 3 + i \) and \( x = 3 - i \). Thus, the zeros of \( g(x) \) are: \[ -2, 3 + i, 3 - i \]