The degree of $f(x)$ is not given. When $f(x)$ is divided by $(x-3)$ the remainder is $15$ and when $f(x)$ is divided by $(x-1)^2$ the remainder is $2x+1$.
Now we need to find the remainder when $f(x)$ is divided by $(x-1)^2(x-3)$.
My attempt : I used remainder theorem and differentiation to obtain the answer $2x^2-2x+3$
Can we find the remainder without using differentiation?