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 \( g(x): \square \)

To find the zeros of the polynomial \( g(x) = x^{3} - 5x^{2} + 12x + 18 \), we can use the Rational Root Theorem to test possible rational roots. Testing values, we find that \( x = -3 \) is a root. We can factor the polynomial using synthetic division by dividing \( g(x) \) by \( x + 3 \), yielding: \[ g(x) = (x + 3)(x^{2} - 8x + 6) \] We then find the roots of the quadratic \( x^{2} - 8x + 6 \) using the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{8 \pm \sqrt{64 - 24}}{2} = \frac{8 \pm \sqrt{40}}{2} = \frac{8 \pm 2\sqrt{10}}{2} = 4 \pm \sqrt{10} \] Thus, the zeros of \( g(x) \) are: \[ -3, 4 + \sqrt{10}, 4 - \sqrt{10} \] The zeros of \( g(x): -3, 4 + \sqrt{10}, 4 - \sqrt{10} \]