SOLUTION: The volume of a rectangular prism is given by the formula V = lwh (length•width•height). What are the length, width, and height of the prism if the volume is 3x3 + 9x2 + 6x? Your a

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The volume of a rectangular prism is given by the formula V = lwh (length•width•height). What are the length, width, and height of the prism if the volume is 3x3 + 9x2 + 6x? Your a      Log On


   

Question 818314: The volume of a rectangular prism is given by the formula V = lwh (length•width•height). What are the length, width, and height of the prism if the volume is 3x3 + 9x2 + 6x? Your answer will not have exact numeric dimensions but rather three algebraic terms that represent them.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E3+%2B+9x%5E2+%2B+6x=3x%28x%5E2%2B3x%2B2%29=3x%28x%2B1%29%28x%2B2%29
So 3x%5E3+%2B+9x%5E2+%2B+6x can be written as the 3-factor product
%283x%29%2A%28x%2B1%29%2A%28x%2B2%29
Maybe the prism your teacher had in mind
(or the prism that the textbook writer had in mind)
has for dimensions
3x , x%2B1 and x%2B2 .
That would be my bet.

However, why not have a prism with dimensions given by
x , 3x%2B3=3%28x%2B1%29 , and x%2B2 ,
or maybe
x , x%2B1 , and 3x%2B6=3%28x%2B2%29 ,
or maybe
sqrt%283%29x , sqrt%283%29x%2Bsqrt%283%29 , and x%2B2 ,
or maybe
x, x%2B1 , and 0.5x%2B1 .
The possibilities are endless.
How limited are the imaginations of the teacher and the textbook writer?