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?
:
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