[tex]D.\:(fg)(x)=3x^3+12x^2-7x-28[/tex]
1) Since this is a question of the algebra of functions and not a composition of functions, we can write this way:
[tex]\begin{gathered} (f\cdot g)(x)=(x+4)(3x^2-7) \\ \\ x\cdot \:3x^2+x\left(-7\right)+4\cdot \:3x^2+4\left(-7\right) \\ \\ (f\cdot g)(x)=3x^3-7x+12x^2-28 \\ \end{gathered}[/tex]
Note that we have applied the Distributive property, also known as FOIL.
Thus, the answer is D
