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Suppose a box is to be constructed from a square piece of material of side length x by cutting out a 2-inch square from each corner and turning up the sides. express the volume of the box as a polynomial in the variable x

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Consider the attached figure. The central square is the "floor" of the box, and it is a (x-2)-by-(x-2) square.

The four rectangles of the side will be the "walls" of the box, and they are (x-2)-by-2 rectangles.

The volume is given by the base area multiplied by the height of the walls, so we have

[tex] \underbrace{(x-2)(x-2)}_{\text{base area}}\times 2 = 2(x^2-4x+4)= 2x^2-8x+8 [/tex]

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shubhamchouhanvrVT

The volume of the box as a polynomial in the variable x will be 2x² - 8x + 8.

What is the volume of the rectangular box?

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units.

The volume of the cuboid is the space occupied by the rectangular box in a three-dimensional space.

Consider the attached figure. The central square is the "floor" of the box, and it is an (x-2)-by-(x-2) square.

The four rectangles of the side will be the "walls" of the box, and they are (x-2)-by-2 rectangles.

The volume is given by the base area multiplied by the height of the walls, so we have

( x - 1) ( x -2 )x 2 = 2 ( x² - 4x + 4 ) = 2x² - 8x + 8

Therefore, the volume of the box as a polynomial in the variable x will be 2x² - 8x + 8.

To know more about volume follow

https://brainly.com/question/15532376

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