ANSWER
[tex] \boxed { C. \: \: \: 5}[/tex]
EXPLANATION
The given functions are
[tex]f(x) = 3 {x}^{2} [/tex]
and
[tex]g(x) = 4 {x}^{3} + 1[/tex]
We are required to find the degree of :
[tex](f \times g)(x) = f(x) \times g(x)[/tex]
[tex](f \times g)(x) = 3 {x}^{2} (4 {x}^{3} + 1)[/tex]
[tex](f \times g)(x) = 12 {x}^{5} + 3 {x}^{2} [/tex]
The degree of this new function is 5.
The correct answer is C.
