SOLUTION: The area of one face of a certain prism is x^2 – 9 square cm. If its volume is x^6 – 729 cubic cm, determine the following: a. height of the prism b. possible length and wi

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The area of one face of a certain prism is x^2 – 9 square cm. If its volume is x^6 – 729 cubic cm, determine the following: a. height of the prism b. possible length and wi      Log On


   

Question 1011292: The area of one face of a certain prism is x^2 – 9 square cm. If its volume is x^6 – 729 cubic cm, determine the following:
a. height of the prism
b. possible length and width of the prism


Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Depends on which face area is the x^2-9. Maybe this face has dimensions (x-9) and (x+9).

Height could be %28x%5E6-729%29%2F%28x%5E2-9%29.

Look at the numerator.
%28x%5E6-729%29=%28x%5E3-27%29%28x%5E3%2B27%29.

%28x-3%29%28x%5E2%2B3x%2B9%29%28x%2B3%29%28x%5E2-3x%2B9%29

The height could be, using that,

highlight%28%28x%5E2%2B3%2B9%29%28x%5E2-3x%2B9%29%29