A box is to be mailed. The volume in cubic inches of the box can be expressed as the product of its three dimensions: V(x) = x^3 - 16x^2 + 79x - 120. The length is (x - 8). Find the linear expressions for the width and the height. Assume that the width is greater than the height.

Question

dumbcow · Answer

Divide V(x) by (x-8).  easiest to use synthetic division

8 |  1   -16    79    -120
             8      -64   120
    --------------------
      1     -8     15      0

leaving x^2 -8x +15
Factor, -5*-3=15  and -5-3=-8
--> (x-5)(x-3)

anonymous · Answer

Thank you. Which one of those would be the width and which would be the height?

dumbcow · Answer

oh right
well width > height
which is greater, x-5 or x-3  ?

anonymous · Answer

oh gosh...umm (x-5)

dumbcow · Answer

say x=10

x-8 = 2
x-5 = 5
x-3 = 7

anonymous · Answer

so (x-3) . Thanks a ton!