Answer: C. [tex]x^4+6x^3-12x-72[/tex]
Step-by-step explanation:
Given functions : [tex]f(x)=\sqrt{x^2+12x+36}[/tex]
[tex]g(x)=x^3-12[/tex]
The function f(x) can also be written as :
[tex]f(x)=\sqrt{x^2+2(6x)+(6)(6)}=\sqrt{(x+6)^2=(x+6)[/tex]
[ ∵ [tex]a^2+2ab+b^2=(a+b)^2[/tex] ]
Now, the product of f(x) and g(x) will be :-
}[tex]f(x)\cdot g(x)=(x+6)(x^3-12)\\\\=x(x^3-12)+6(x^3-12)\\\\=x^4-12x+6x^3-72\\\\=x^4+6x^3-12x-72[/tex]
