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Let g(x)g(x) g(x) denote a quintic (5th\big(5^\text{th}(5th-degree)\big)) polynomial such that g(n)=2ng(n) = 2^ng(n)=2n for n=1,2,3,4,5n = 1,2,3,4,5n=1,2,3,4,5 and g(x)g(x) g(x) has a constant term of 5!5!5!.
Find g(6)g(6) g(6).
Bonus: Generalize this.
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