Question

I’m confused. What is the correct answer choice? and an explanation

Answer 1

`D.\:(fg)(x)=3x^3+12x^2-7x-28`

1) Since this is a question of the algebra of functions and not a composition of functions, we can write this way:

`\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}`

Note that we have applied the Distributive property, also known as FOIL.

Thus, the answer is D