Solution
= Solution
Use the nodes in the order $0,1,2,3$. Their first <divided difference>[divided differences] are $4,-2,6$, their second divided differences are $-3,4$, and their third divided difference is $7/3$. The <Newton interpolation polynomial> is therefore
$$
\boxed{
p_3(x)=4x-3x(x-1)+\frac73x(x-1)(x-2)
}.
$$
This is the unique <polynomial interpolation>[interpolating polynomial] of degree at most three through the four data points.