I've already vaguely given you the answer
Algebra
Level
5
Let \(g(x) \) denote a quintic \(\left(5^\text{th} \text{ degree}\right)\) polynomial such that \(g(n) = 2^n\) for \(n = 1,2,3,4,5\) and \(g(x) \) has a constant term of \(5!\). Find \(g(6) \).
Bonus: Generalize this.
by
Pi Han Goh