We have a polynomial $f(x)$ with rational roots that leaves remainders $15, 2x + 1$ when divided by the polynomials $x - 3, (x-1)^2$ respectively. What is the remainder when $f(x)$ is divided by $(x - 3)(x-1)^2$?
From the remainder theorem we know that,
$f(3) = 15$.
I thought quite hard about this and tried various methods, but couldn't come up with anything useful.