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)?
since a is a constant, it can't change the degree.
So our answer is the highest degrees of f(x) + g(x).
That's basically the highest degree in f(x) of g(x).
The highest degree in g(x) = 8 (2x^8)
and the highest degree in f(x) = 4 (x^4)
So our answer is 8, since 8 > 4.
I hope this helped. :))