Lucy cuts 4 squares with side length x in. from the corners of a 12 in. by 18 in. cardboard rectangle. she folds the remaining cardboard to make a tray that is x in. high. write and simplify a polynomial function for the volume v of the tray in terms of x. , i am loosing a braincell each day

Volume of tray =

Step-by-step explanation:

The Dimensions of rectangular cardboard is given by 12 inches by 18 inches

Length of the rectangular cardboard = 18 inches

Width of the rectangular cardboard = 12 inches

if the square of sides x inches is cut from each corner of the rectangular cardboard and folded to make a tray, then we have

Length of the tray = length of cardboard - 2 (side of the square )

                               =

Width of the tray = width of cardboard - 2( side of square)

                            =

height of tray = sides of square

                       = x

volume of tray = Length × width × height

Volume of tray =

first we multiply (12-2x) and (18-2x)

Volume of tray =

                         =

                         =

                         =

Hence the volume of tray =

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or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!