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Question 53710: This question is from the University of Phoenix math book:
Decreasing cube. Each of the three dimensions of a cube with a volume of y3 cubic centimeters is decreased by a whole number of centimeters. Of the new volume is y3 - 13y2 + 54Y - 72 cubic centimeters and the new width is y - 6 centimeters, then what are the new length and height?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Decreasing cube. Each of the three dimensions of a cube with a volume of y3 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?
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We can find value of the length times the height by dividing y^3-13y^2+54y-72 by (y-6), an easy operation using synthetic division
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: --------------------
+6 | 1 - 13 + 54 - 72
.............+ 6 - 42 + 72
....----------------------
..........1 - 7 + 12 + 0 (used "..." to get everything to line up)
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Result of this is: 1 - 7 + 12 which is: y^2 - 7y + 12
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This easily factors to: (y-3)(y-4) = 0
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Length = +4; Width = +3
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Check if you mult (y-6)*(y-3)*(y-4) should give you: y^3 - 13y^2 + 54y - 72
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