Mathematics: Arectangular box is x feet long and x feet wide. the volume of the box is (4x^8 + 3x^6) cubic ft. what polynomial represents the height of the box in feet?

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Arectangular box is x feet long and x feet wide.

saren47

10.01.2022

Hence, the height, in feet, of the rectangular box is given by the polynomial h=4x^6+3x^4

Step-by-step explanation:

The volume of a rectangular box is given by the formula:

V=length*width*height

We are given V=4x^8+3x^6 , length = x, and width = x , plugging these into the formula and figuring out height:

$V=length*width*height\\4x^8+3x^6=(x)(x)(h)\\4x^8+3x^6=x^2h\\h=\frac{4x^8+3x^6}{x^2}\\h=\frac{x^2(4x^6+3x^4)}{x^2}\\h=4x^6+3x^4$

Hence, the height, in feet, of the rectangular box is given by the polynomial h=4x^6+3x^4

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