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

Answer:

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

Step-by-step 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 $(2x+5)$