jmc

Question

We have that 3 f(x) + 4 g(x) = h(x) where f(x), g(x), and h(x) are all polynomials in x. If the degree of f(x) is 8 and the degree of h(x) is 9, then what is the minimum possible degree of g(x)?

Accepted Answer

If the degree of h(x) is 9, that means there is a x^9 term in h(x). That term cannot come from f(x), since its degree is 8, so it must come from g(x). That means the degree of g(x) has to be at least 9, and indeed, it can only be 9.