An algebra problem by Pankaj Joshi

Algebra Level 5

A polynomial f(x)f(x) with rational coefficients leaves remainder 1515 when divided by x3x-3 and remainder 2x+12x +1 when divided by (x1)2(x-1)^2. If f(x)f(x) is divided by (x3)(x1)2(x-3)(x-1)^2, then the remainder is r(x)r(x) . What is the value of r(5)r(5).

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