Let f(x) be a quadratic polynomial such that f(-4)=-22, f(-1)=2, and f(2)=-1. Let g(x)=f(x)^16. Find the sum of the coefficients of the terms in g(x) that have an even degree. (For example, the sum of the coefficients of the terms in -7x^3+4x^2+10x-5 that have an even degree is (4)+(-5)=-1.)
P.S. I would appreciate it if I could get a detailed explanation and not just answer since I would like to learn, but it's fine if that doesn't happen.