Question

A carpenter is making a wooden box which must hold a volume of y cubic inches. The length of its rectangular base will be one inch longer than its width, x. The depth of the chest will be two inches longer than the longest side of the base. Which equation represents the volume of the chest? y=x3+4x2+3x y=x3+3x2+2x y=x2+3x+2 y=x2+4x+3

Answer 1

Answer: I believe it is x^3 + 4x^2 + 3x

Explanation:

x(x+1)(x+3) =

x(x^2 + 4x + 3)=

x^3 + 4x^2 + 3x

Answer 2

The correct option is 1.

Explanation:

It is given that the volume of a wooden box is y cubic inches.

Let x be the width of the base.

The length of its rectangular base will be one inch longer than its width x.

Length of the box = (x+1) inches

The depth of the chest will be two inches longer than the longest side of the base.

Depth = (x+1) + 2 = (x+3) inches

Volume of a rectangular box is

`V=length * breadth* height`

Volume of the chest is

`y=(x+1) * x* (x+3)`

`y=(x^2+x)* (x+3)`

On further simplification, we get

`y=x^2(x+3)+x(x+3)`

`y=x^3+3x^2+x^2+3x`

Combine like terms.

`y=x^3+4x^2+3x`

Therefore the correct option is 1.