A polynomial $f(x)$ gives remainder $2$ when divided by $(x-3)$ and gives a remainder $-4$ when divided by $(x+1)$. What is the remainder when $f(x)$ is divided by $(x^2 - 2x - 3)$?
I have shortened the question by:
1.Showing that $f(-1) = -4$ and $f(3) = 2$ by remainder theorem respectively.
2.Figured out that $(x^2 - 2x - 3)= (x-1)(x-3)$.