SOLUTION: Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters

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Question 202842:
Decreasing cube. Each of the three dimensions of a
cube with sides of length s centimeters is decreased by a
whole number of centimeters. The new volume in cubic
centimeters is given by
V(s) = s3 - 13s2 + 54s - 72.
a) Find V(10).
b) If the new width is s - 6 centimeters, then what are the
new length and height?
c) Find the volume when s = 10 by multiplying the
length, width, and height.
Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
V(s) = s^3 -13s^2 +52s-72
.
V(10) = (10)^3 -13(10)^2+54(10) -72
V(10)= 1000-1300+540 -72
V(10)= 168
.
If one side is (s-6),, divide total by (s-6) to find multiple of 2 remaining sides
.
,,,6,,,,,,1,,,,-13,,,,+54,,,,-72
,,,,,,,,,,,,,,,,,6,,,,-42,,,,+72
__________________________________
,,,,,,,,,,1,,,,,-7,,,,+12,,,,,0
.
(x-6)(x^2 -7x +12),,,,,,,,factor
.
(x-6)(x-3)(x-4),,,,,,,,def of three new sides
.
@s=10,,,,(10-6)(10-3)(10-4),,,4*7*6 = 168,,,,ok