Answer:
C. V(x) = 2x^3 + 12x^2 + 22x + 12
Step-by-step explanation:
The volume of a fish tank is the multiplication of the area of the base by the height.
In this question:
Area of the base: [tex]B(x) = 2x^{2} + 6x + 4[/tex]
Height: [tex]H(x) = x + 3[/tex]
Volume:
[tex]V(x) = B(X)*H(x) = (2x^{2} + 6x + 4)(x + 3) = 2x^{3} + 6x^{2} + 4x + 6x^{2} + 18x + 12 = 2x^{3} + 12x^{2} + 22x + 12[/tex]
So the correct answer is:
C. V(x) = 2x^3 + 12x^2 + 22x + 12