Suppose a box is to be constructed from a square piece of ma

Suppose a box is to be constructed from a square piece of material of side length x by cutting out a 3-inch square from each corner and turning up the sides. Express the volume of the box as a polynomial in the variable x. Volume =

Solution

side length of square meterial is x

3 inch square is cut from each corner

now the length of box = x - 6

width = x- 6

height = 3

volume of box = length * width * height

volume = (x-6)(x-6)* 3

= 3 ( x^2 -12x + 36 )

volume = 3x^2 -36x + 108