Posted by **Sandra** on Friday, July 10, 2009 at 3:06pm.

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

- algebra -
**Marth**, Friday, July 10, 2009 at 3:20pm
a) use 10 for s.

V(10) = 10^3 - 13(10)^2 + 54(10) - 72

V(10) = 1000 - 1300 + 540 - 72

V(10) = 168

b) Divide V(s) by (s-6)

Using synthetic division:

6| 1 |-13 | 54 | -72

| 0 | 6 | -42 | 72

_____________________

| 1 | -7 | 12 | 0

So, the new length and height can be found by s^2 -7s + 12.

That can factored into (s-3)(s-4)

V(s) = (s-6)(s-3)(s-4)

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