The volume of a rectangular prism is represented by the function x^3+9x^2+6x-16.the length of the box is x+2,while the height is x+8.find the expression representing the width of the box

The correct answer is:  width b = x - 1

Step-by-step explanation:

Given:

Polynomial function or cubic equation which represents the volume of the rectangular prism   P(x) = x³ + 9 x² + 6 x - 16

The formula to calculating volume of the rectangular prism is:

V = a · b · c   Where a is length of the base, b width of the base and c is height

In this case  a = x + 2, c = x + 8 and b = ?

We can factorize the given equation using the Bezu theorem :

P(1) = 1³ + 9·  1² + 6 · 1 - 16 = 0

This means that the polynomial is divided by the binomial (x - 1) without residue.

We will divide polynomial function with binomial (x - 1)

(x³ + 9 x² + 6 x - 16) : (x - 1) = x² + 10 x + 16

When we multiply  a · c = (x + 2) (x + 8) = x² + 10 x + 16

We have formula V = a · b · c,  from which we conclude that

width is b = (x - 1)

The second solution is to divide P(x) with a · c = (x + 2) (x + 8) = x² + 10 x + 16

and get b = (x - 1)

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