SOLUTION: Please help me to solve this word problem: Decreasing cube: Each of the three dimensions of a cube with a volume of y^3 cubic centimeters is decreased by a whole number of cent

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Question 87060: Please help me to solve this word problem:
Decreasing cube: Each of the three dimensions of a cube with a volume of y^3 cubic centimeters is decreased by a whole number of centimeters if the new volume is y^3-13y^2+54y-72 cubic centimeters and the new width is y-6 centimeters, then what are the new length and height?
Thank you
Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!
If the original cube had a height, width, and length of units and a the width decreased by 6 to make a new cube, wouldn't each side be units? ... This must be a rectanguler prism. ...
y^3 - 13y^2 + 54y - 72 = height * width * length
y^3 - 13y^2 + 54y - 72 = height * (y - 6) * length
(y^3 - 13y^2 + 54y - 72) / (y - 6) = height * length
Synthetic Division being the fastest (if you do not know how to do this procedure, do the long division):
6 | ..... 1 ...... -13 ...... 54 ...... -72
............1...........-7.........12..........0
y^2 - 7y + 12 = height * length
(y - 4)(y - 3) = height * length
y - 4 is either a height or a length
y - 3 is either a length or a height