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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