A Polynomial Remainder

Algebra Level 5

A polynomial f(x)f(x) with rational coefficients leaves a remainder of 15 when divided by x3,x-3, and leaves a remainder of 2x+12x+1 on division by (x1)2.(x-1)^{2}. The remainder when this polynomial is divided by (x3)(x1)2(x-3)(x-1)^{2} is of the form ax2+bx+c. ax^{2}+bx+c. Find the value of abc.-abc.

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

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