### Instruction: Find the remainder when $x^3-3x^2-9x+30$ is divided by $x-3$.### Response: One way to approach this problem is to use polynomial long division or synthetic division and find the quotient and remainder of the division.
However, there is a faster and simpler way to find the remainder without finding the quotient.
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 $27-27-27+30=3$.