If f (x) = 3^2 and g (x) = 4x^3+1, what is the degree of (f*g) (x) ?

I'm assuming you meant to say f (x) = 3x^2. If that assumption is correct, then the degree is found by multiplying the leading terms from both f (x) and g (x). The leading terms are 3x^2 and 4x^3

3x^2*4x^3 = (3*4) * (x^2*x^3) = 12x^ (2+3) = 12x^5

The exponent of that result is 5, so the degree of (f*g) (x) is 5

Answer: 5