a. The degree of the polynomial \(p(x)\) is \(11\), and the degree of the polynomial \(q(x)\) is \(7\). Find all possible degrees of the polynomial \(p(x) + q(x)\).
b. Suppose \(f\) is a polynomial such that \(f(0) = 47\), \(f(1) = 32\), \(f(2) = -13\), and \(f(3)=16\). What is the sum of the coefficients of \(f\)?
