Problem
ALG-B1-M11-P009 Polynomial value
#9
★★☆☆☆ Level 2 of 5
\(P\) has degree at most \(2\), \(P(0)=2\), \(P(1)=5\), \(P(2)=10\). Find \(P(3)\).
Look at second differences.
The first differences are \(3,5\), so the second difference is \(2\). The next first difference is \(7\), hence \(P(3)=17\).
Strategy: degree controls differences.