Remainder Theorem for Polynomials

Here is a problem presented in a video by Eddie Woo. Try solving it yourself and then watch Eddie Woo solve it in the solution below. $$\\$$ $P(x)$ is a polynomial of degree greater than $3$. When $P(x)$ is divided by $x-3$, the remainder is $1$; when divided by $x+2$, the remainder is $-9$. What is the remainder when $P(x)$ is divided by $(x-3)(x+2)$?