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) with even exponents. (For example, the sum of the coefficients of the terms in -7x^3 + 5x^2 + 10 with even exponents is 5 and 10).
Whoever answers this, thanks for putting in time and effort to help strangers. Nothing but respect for you guys! Sorry I couldnt turn into latex. I am in no rush, but if you could finish in a week that would be nice.