Let f(x) = x^4 - 3x^2 + 2 and g(x) = 2x^8 - 6x^2 + 2x - 1. What is the degree of f(x)*g(x)?
This would result in a x4 multiplied by a 2x8 for the highest degree 2 x4+8 = 2 x12 for degree 12