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.