Find the remainder when $x^3-3x^2-9x+30$ is divided by $x-3$.
One way to approach this problem is to use polynomial long division or synthetic division and find the quotient and remainder of the division. This is based on the remainder theorem, which says that the remainder of dividing a polynomial $f(x)$ by $x-a$ is equal to $f(a)$. In this case, we are dividing by $x-3$, so $a=3$. To find the remainder, we just need to plug in $x=3$ into the polynomial and simplify. So the remainder is $(3)^3-3(3)^2-9(3)+30$. Expanding and simplifying, we get $27-27-27+30=3$. 