# Nicolae's polynomial division

Algebra Level 5

$$P(x)$$ is a polynomial of degree 7 such that $$P(2)=35,\,P(3)=25$$ and $$P(5)=23$$. Let $$U(x)$$ be the remainder of $$P(x)$$ upon division by $$(x-2)(x-3)(x-5)$$. Evaluate $$U(1)$$.

This problem is posed by Nicolae S.

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