Question

A rectangular box is twice as long as it is wide. The height of the box is 3 feet less than the width. If the box is x feet wide, what polynomial represents its volume in cubic feet?

A)4x-3
B)2x^3+6^2
C)2x^2-6x
D)2x^3-6x^2

Answer 1

`V=2x^3-6x^2`

D is the correct option.

Explanation:

The width of the box is x feet.

Height of the box is 3 feet less than the width.

Hence, height = x - 3

Now, box is twice as long as it is wide.

Length = 2x

Volume of the box is given by

Volume = length × width × height

Substituting the known values,

V = 2x(x)(x-3)

On simplifying, we get

`V=2x^2(x-3)\\V=2x^3-6x^2`

Hence, D is the correct option.

Answer 2

In order to get the volume of a rectangular box, the formula would be V = LxWxH.
So given that Length L = 2w
H = 3-w
W = x
Let x be the width, so it will look like this.
V = (2x)(x-3)(x)
Multiply these and we will get 2x^3-6x^2.
Therefore, the answer would be option D. Hope this answer helps. Let me know if you need more help next time.