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

The length of the rectangular prism obtained by finding the quotient of the volume divided by the product of height and width. Hence, the length of the box is x + 4

The volume of a rectangular prism is given calculated using the formula :

Volume = Length × width × height

From the formula :

Length =

Width × height = (x - 1)(x + 8)

(x - 1)(x + 8) = x² + 8x - x - 8

= x² + 7x - 8

Using long divison :

______ | x + 4

______ | _______________

x²+7x-8 | x³ + 11x² + 20x – 32

______ | x³ + 7x² - 8x

-______| ___ 4x²+28x

___________4x²+28x - 32

-___________0__0 ___0

Therefore, the quotient, which is the value of the length of the rectangular prism ls x + 4

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we know that

the volume of a rectangular prism is equal to

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

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

so

therefore

the answer is

the length of the box is equal to

the answer is 5636.7

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