Problem
ALG-B1-M10-P012 Three polynomial values
#12
★★★☆☆ Level 3 of 5
A polynomial \(P(x)\) of degree at most \(2\) satisfies \(P(0)=1\), \(P(1)=3\), \(P(2)=7\). Find \(P(3)\).
For a quadratic polynomial, second differences are constant.
The first differences are \(2\) and \(4\), so the second difference is \(2\). The next first difference is \(6\). Therefore \(P(3)=7+6=13\).
Polynomials can be handled without solving for all coefficients.