Let f(x) = x^4-3x^2 + 2 and g(x) = 2x^6 - 6x^2 + 2x -1. Let a be a constant. What is the largest possible degree of f(x) + a*g(x)?
The largest degree of f(x) is 4.
The largest degree of g(x) is 6
Multiplying g(x) by a constant does not increase the degree of g(x).
Adding together these polynomials give a result whose highest degree is 6.