The table shows the functions representing the height and the area of the base of a rectangular prism for different values of x.

The volume of the prism when x = 3 is 36. Which equation can be used to represent the volume of the prism, V(x)?

V(x) = (f ∙ g)(x)
V(x) = (g + f)(x)
V(x) = (f – g)(x)
V(x) = (g – f)(x)

V(x) = (f ∙ g)(x)

Step-by-step explanation:

Note. There is no table attached.

However it can solved with remaining information given.

The volume of a prism is

If we have a function for the volume V(x) it has to be equal to a product of functions for the area and the height

Therefore the function will be similar to:

So the correct option is the first one

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

597

step-by-step explanation: