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Let h(x)h(x) h(x) denote a monic 8th8^\text{th} 8th-degree polynomial such that h(m)=(m6)h(m) = \binom m6 h(m)=(6m) for m=6,7,8,…,13m = 6,7,8,\ldots,13m=6,7,8,…,13.
Find h(5)h(5) h(5).
Notation: (mn) \binom mn (nm) denotes the binomial coefficient (mn)=m!n!(m−n)! \binom mn = \frac{m!}{n!(m-n)!} (nm)=n!(m−n)!m! for non-negative integers m≥nm\geq n m≥n.
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