We have that 3f(x) + 4g(x) = h(x) where f(x), g(x), and h(x), are all polynomials in x. If the degree of f(x) is 2 and the degree of h(x) is 8, then what is the minimum possible degree of g(x)?

Since there is a sum of polynomials and the sum is of degree 8, at least one of the polynomials f(x) and g(x) must be of degree 8.

Since the degree of f(x) is 2, the degree of g(x) must be 8.

The coefficients, 3 and 4, have no influence upon this problem.