SOLUTION: A open tray is to be made from a 8.5-inch by 12-inch piece of sheet metal by cutting squares of equal size from each corner and bending up the flaps, write a formula for the volume

Question 623310: A open tray is to be made from a 8.5-inch by 12-inch piece of sheet metal by cutting squares of equal size from each corner and bending up the flaps, write a formula for the volume of the tray as a polynomial function...I think it starts out like this V(x)=4x(12-2x)(8.5-2x) but Im not sure.
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Except for the 4, your formula is exactly correct. The general formula for volume of this shape (rectangular prism) is:
V = l*w*h
You got the length and width right. But the height is just x, not 4x. So the volume of your tray is:
V(x)=x(12-2x)(8.5-2x)

This is not a polynomial, however. So we need to multiply it out. Distributing the x we get:

Now we use FOIL to multiply the rest:

Simplifying...

Normally we write polynomials in order from highest exponent to lowest:

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