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15 April, 13:11

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

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  1. 15 April, 16:32
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    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)

    God with you!
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