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 centimete

Algebra ->  Customizable Word Problem Solvers  -> Misc -> 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 centimete      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 141919: 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) About Me  (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?
:
Use synthetic division to divide the new volume by the width
:
....__________________
+6|1 - 13 + 54 - 72
..........+ 6 - 42 + 72
.......----------------
......1 - 7 + 12 + 0
That gives us:
y^2 - 7y + 12 = 0
Factors to
(y-4)(y-3) = 0
:
y = 4, y = 3; the length and height