A Polynomial Remainder

Algebra Level 5

A polynomial $f(x)$ with rational coefficients leaves a remainder of 15 when divided by $x-3,$ and leaves a remainder of $2x+1$ on division by $(x-1)^{2}.$ The remainder when this polynomial is divided by $(x-3)(x-1)^{2}$ is of the form $ax^{2}+bx+c.$ Find the value of $-abc.$

Note- This question is an adaptation of a previous math contest question.