Curious Remainders

Algebra Level 4

A degree $$5$$ polynomial $$P(x)$$ has the property that the remainder when $$P(x)$$ is divided by $$(x-a)$$ is $$a$$ for $$a=1\rightarrow 5$$. If $$P(0)=-1$$, find the value of $$P(12)$$.

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