What represents the remainder of $P(x)$

Question

A polynomial is divided by $(x-3),$ which of the following would represent the remainder?

1. $P(x+3)$
2. $P(0)$
3. $P(-3)$
4. $P(3)$

I believe the answer is $P(3)$ because $x-3=0$ equals $x=3$ when making it equal zero.

But I'm not completely sure, and feel like this wasn't covered well enough in class. If you could help me understand how to complete questions like this I'd be grateful.

Answer 1

Remainder theorem. As you say, if P were simply $x−3$ then the remainder would be $0= P(3)$, hence #4 is the only one that can be right.