Question

The volume of a rectangular prism is represented by the function x3 + 11x2 + 20x – 32. The width of the box is x – 1 while the height is x + 8. Find the expression representing the length of the box

Answer 1

we know that

the volume of a rectangular prism is equal to

$V=L*W*H$

where

L is the length of the box

W is the width of the box

H is is the height of the box

in this problem we have

$V=x^{3\ }+11x^2+20x-32$

$W=x-1$

$H=x+8$

$L=?$

Find the length of the box

Using a graph tool-------> we will determine the roots of the equation of volume

see the attached figure

the roots are

$x=-8\\x=-4\\ x=1$

so

$x^{3\ }+11x^2+20x-32=(x+8)*(x+4)*(x-1)$

therefore

the answer is

the length of the box is equal to $(x+4)$

Answer 2

Answer: length is x+4

Step-by-step explanation:

Check attachment for details