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algebra

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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 - ,

    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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