SOLUTION: Each of the 3 dimensions of a cube with a volume of y^3 cubic centemeters is decreased by a whole number of centimeters. If the new volume is y^3 - 13y^2 + 54y

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Question 120391: Each of the 3 dimensions of a cube with a volume of y^3 cubic centemeters 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?
Answer by ankor@dixie-net.com(22740) (Show Source):
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Each of the 3 dimensions of a cube with a volume of y^3 cubic centemeters 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?
:
We know that (y-6) is a factor of x^3 - 13x^2 + 54x - 72
:
Use synthetic division:
....._________________
6 | 1 - 13 + 54 - 72
..............6 - 42 + 72
....-----------------
.......1 - 7 + 12
:
So we have:
y^2 - 7y + 12 = 0
Factors to
(y-4)(y-3) = 0
:
The new length = 4
The new height = 3

SOLUTION: Each of the 3 dimensions of a cube with a volume of y^3 cubic centemeters is decreased by a whole number of centimeters. If the new volume is y^3 - 13y^2 + 54y - 72 cubic centimet