Question

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

Answer 1

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