ind all zeros of the function \( f(x)=6 x^{3}-25 x^{2}+2 x+8 \). Enter the zeros separated by commas.

To find the zeros of the function \( f(x) = 6x^3 - 25x^2 + 2x + 8 \), we can use the Rational Root Theorem to test for possible rational roots. After evaluating various potential candidates, we find that \( x = 2 \) is a root. Next, we can perform polynomial long division or synthetic division to simplify \( f(x) \) after factoring out \( (x - 2) \). We will find that the quotient is \( 6x^2 - 13x - 4 \). Next, we can apply the quadratic formula to solve \( 6x^2 - 13x - 4 = 0 \): \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{13 \pm \sqrt{(-13)^2 - 4(6)(-4)}}{2(6)} \] \[ x = \frac{13 \pm \sqrt{169 + 96}}{12} = \frac{13 \pm \sqrt{265}}{12}. \] Thus, the zeros of the function \( f(x) \) are: \[ x = 2, \quad x = \frac{13 + \sqrt{265}}{12}, \quad x = \frac{13 - \sqrt{265}}{12}. \] In conclusion, the zeros are: \[ 2, \frac{13 + \sqrt{265}}{12}, \frac{13 - \sqrt{265}}{12}. \]