Problem
ALG-B1-M12-P030 Variant 8, Problem 2
#30
★★★★★ Level 5 of 5
A polynomial of degree \(\le3\) has values \(0,1,8,27\) at \(0,1,2,3\). Find \(P(4)\).
This is a cubic sequence.
Differences \(1,7,19\), second \(6,12\), third \(6\). Next: second \(18\), first \(37\), value \(64\).
Mock olympiad problem. Tags: polynomial-values.