A rectangular prism has a volume of V= 2x^3+6x^2+4x. What could the dimensions of this prism be?

1 Answer
Jul 29, 2015

Answer:

#2x^3+6x^2+4x = 2x(x+1)(x+2)#

So some possible dimensions are:

#2x xx (x+1) xx (x+2)#

#x xx 2(x+1) xx (x+2)#

#x xx (x+1) xx 2(x+2)#

Explanation:

#2x^3+6x^2+4x = 2x(x^2+3x+2) = 2x(x+1)(x+2)#

I find these kind of questions rather strange, as they place no real limitations on the dimensions apart from the total volume.

In fact, given any #a, b > 0#, let #c=(2x^3+6x^2+4x)/(ab)#

Then a rectangular prism of sides #a#, #b# and #c# has the required volume.