Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^8 - 6x^2 + 2x -1. Let a be a constant. What is the largest possible degree of f(x) + a* g(x)?
Multiplying a polynomial by a non-zero constant does not change its degree
f(x) + a * g(x) = 8th degree = greatest possible degree