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)?

Multiplying by a constant does not change the degree of the polynomial...

So degree of. f+ a* g. would still be 8