A former colleague Bill Wardlaw (March 3, 1936-January 2, 2013) used to create a “Problem of the Week” for his US Naval Academy students, giving a prize of a cookie if they could solve it. One of them is given below.

Suppose *p* and *q* are each monic polynomials of degree *4* with real coefficients and the intersection of their graphs is *{(1, 3), (5, 21)}*. If *p(3) – q(3) = 20*, what is the area enclosed by their graphs?