For a polynomial $p(x)$, value of $p(3)$ is $-2$

Question

SAT prep problem. (I am not taking the SATs and so it is embarrassing that I can't solve this). Which of the following must be true about $p(x)$?

A. $x-5$ is a factor of $p(x)$

B. $x-2$ is a factor of $p(x)$

C. $x+2$ is a factor of $p(x)$

D. The remainder when $p(x)$is divided by $x-3$ is $-2$.

Since I don't what to do, I took an example. $p(x) = x^2 - 3x - 2$.

$p(3) = -2$

Then what?

Answer 1

If $p(3)=-2$ then $3$ will be the root of polynomial $g(x)=p(x)+2$ so $g(x)=(x-3)q(x)$. This leaves option $D$.