Question

The base of a box, built from a model, has an area that can be represented by the function B(x) = 4x^2 + 8, where x is the width of the model's base. The height of the box can be represented by the function H(x) = x + 2.

Which function best describes C(x), the capacity of the box?

A. C(x) = 4x^3 + 8x^2 + 8x + 16
B. C(x) = 4x^3 + 16
C. C(x) = 4x^3 + 16x^2 + 16
D. C(x) = 4x^3 + 32x^2 + 2x + 16

Answer 1

A) C(x)=4x³+8x²+8x+16

Explanation:

(4x²+8)(x+2)=

A) 4x³+8x²+8x+16

Answer 2

The capacity of the box would be the volume.

Multiply the area by the height:

4x^2 + 8 times x+2

Multiply each term by each term:

4x^2 * x = 4x^3

4x^2 * 2 = 8x^2

8 * x = 8x

8*2 = 16

Combine the terms to get:

4x^3 + 8x^2+ 8x +16

The answer is A. C(x) = 4x^3 + 8x^2 + 8x + 16