1. **Problem:** Find the possible rational zeros of the function $f(x) = 3x^2 + 2x - 1$ using the Rational Root Theorem. 2. **Rational Root Theorem:** Possible rational zeros are of the form $\pm \frac{p}{q}$ where $p$ divides the constant term and $q$ divides the leading coefficient. 3. For $f(x) = 3x^2 + 2x - 1$: - Constant term $= -1$, divisors: $\pm 1$ - Leading coefficient $= 3$, divisors: $\pm 1, \pm 3$ 4. Possible rational zeros: $$\pm \frac{1}{1}, \pm \frac{1}{3}$$ which simplifies to $$\pm 1, \pm \frac{1}{3}$$ 5. **Final answer:** The short list of possible rational zeros is $\boxed{\pm 1, \pm \frac{1}{3}}$.