SOLUTION: 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

Question 98190: 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?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
:
Divide (y-6) into y^3 - 13y^2 + 54y - 72 using synthetic division:
:
....____________________
6 |1 - 13 + 54 - 72
.....0 + 6 - 42 + 72
....------------------
.....1 - 7 + 12 + 0
:
This gives us a quotient of:
y^2 - 7y + 12
:
Which factors to:
(y - 3)(y - 4); the new height and length
:
:
you can check solution by (y-6)*(y-3)*(y-4)

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