1. **State the problem:** We have a cubic polynomial function $g(x)$ such that $g(\frac{2}{3})=0$ and $g(0)=5$. We need to determine which of the given options must be a factor of $g(x)$. 2. **Recall the factor theorem:** If $g(a)=0$ for some number $a$, then $(x - a)$ is a factor of $g(x)$. 3. **Apply the factor theorem:** Since $g(\frac{2}{3})=0$, the factor corresponding to this root is $x - \frac{2}{3}$. 4. **Rewrite the factor to match options:** Multiply both sides by 3 to clear the fraction: $$3\left(x - \frac{2}{3}\right) = 3x - 2$$ 5. **Check the options:** Option C is $3x - 2$, which matches the factor derived from the root. 6. **Verify $g(0)=5$ does not affect the factor:** The value at zero does not determine the factor but confirms the polynomial is not zero at $x=0$. **Final answer:** The factor must be $3x - 2$ (Option C).