An algebra problem by Pankaj Joshi

Algebra Level 5

A polynomial \(f(x)\) with rational coefficients leaves remainder \(15\) when divided by \(x-3\) and remainder \(2x +1\) when divided by \((x-1)^2\). If \(f(x)\) is divided by \((x-3)(x-1)^2\), then the remainder is \(r(x)\) . What is the value of \(r(5)\).

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