1. List the possible rational zeros of: \[ f(x)=6 x^{3}+11 x^{2}-37 x+3 \]

Step 1 ：Given the polynomial function \(f(x)=6 x^{3}+11 x^{2}-37 x+3\).

Step 2 ：According to the Rational Root Theorem, if a polynomial has a rational root, then it must be a factor of the constant term divided by a factor of the leading coefficient.

Step 3 ：In this case, the constant term is 3 and the leading coefficient is 6. So, the possible rational roots are factors of \(\frac{3}{6} = \frac{1}{2}\).

Step 4 ：The factors of the constant term 3 are 1 and 3.

Step 5 ：The factors of the leading coefficient 6 are 1, 2, 3, and 6.

Step 6 ：Therefore, the possible rational roots are 1, 3, \(\frac{1}{2}\), \(\frac{3}{2}\), \(\frac{1}{6}\), and \(\frac{1}{3}\).

Step 7 ：Final Answer: The possible rational zeros of the function \(f(x)=6 x^{3}+11 x^{2}-37 x+3\) are \(\boxed{1, 3, \frac{1}{2}, \frac{3}{2}, \frac{1}{6}, \frac{1}{3}}\).