Question

The formula for volume of this rectangular prism is: v=2x^3+17x^2+46x+40 find an expression for the missing side length. Show all of your work for full credit.

Answer 1

the missing side length is
`(2x+5)`

Explanation:

we know that the volume of the rectangular prism is equal to

`v=LWH`

In this problem we have

`v=L(x+4)(x+2)`

`v=2x^3+17x^2+46x+40`

using a graphing tool find the x-intercepts of the function

see the attached figure

The x-intercepts are

`x=-4, x=-2.5, x=-2`

so

`v=2(x+2.5)(x+4)(x+2)`

`v=(2x+5)(x+4)(x+2)`

therefore

the missing side length is
`(2x+5)`