Question 2 For a certain polynomial $P(x), P(3)=2$ and $P(-1)=-1$. Use this information to deduce the remainder when $P(x)$ is divided by $(x-3)(x+1)$.

Step 1 ：By the Remainder Theorem, we have $P(3) = 2$ and $P(-1) = -1$.

Step 2 ：Let $Q(x)$ and $ax + b$ be the quotient and remainder, respectively, when the polynomial $P(x)$ is divided by $(x - 3)(x + 1)$, so $P(x) = (x - 3)(x + 1) Q(x) + ax + b$.

Step 3 ：Setting $x = 3$, we get $P(3) = 3a + b$, so $3a + b = 2$.

Step 4 ：Setting $x = -1$, we get $P(-1) = -a + b$, so $-a + b = -1$.

Step 5 ：Solving the system of equations, we find $a = 1$ and $b = -3$.

Step 6 ：Therefore, the remainder is \(\boxed{x - 3}\).