A rectangular prism has a volume of

Question

4x(cubed) + 30 x(squared) +36x. What linear expressions can represent possible dimensions of the prism?

Please explain.

Answer 1

The volume factors into four linear factors:
2x(x+6)(2x+3)
Since we need three values for the dimensions of the prism, so there are
C(4,2)=6 sets of dimensions, i.e. choose 2 factors out of 4 to reduce to one dimension. The two other dimensions will be used as is.
Example dimensions are:
2x (x+6) (2x+3)
2 x(x+6) (2x+3)
x 2(x+6) (2x+3)
...
up to 6 sets.