1. **State the problem:** We are given that $P(x) = Q(x) \cdot (x - 3)$ and asked which of the statements A, B, C, or D must be true. 2. **Recall the property of multiplication:** If $P(x) = Q(x) \cdot (x - 3)$, then for any value of $x$, $P(x)$ is the product of $Q(x)$ and $(x - 3)$. 3. **Evaluate $P(3)$:** Substitute $x = 3$ into the equation: $$P(3) = Q(3) \cdot (3 - 3) = Q(3) \cdot 0 = 0$$ This means $P(3) = 0$ regardless of the value of $Q(3)$. 4. **Check other options:** - A. $P(0) = 3$ is not necessarily true because $P(0) = Q(0) \cdot (0 - 3) = Q(0) \cdot (-3)$, which depends on $Q(0)$. - B. $Q(0) = 3$ is not necessarily true; no information guarantees this. - D. $Q(3) = 0$ is not necessarily true; $Q(3)$ can be any value since it is multiplied by zero in $P(3)$. **Final answer:** C. $P(3) = 0$ must be true.