how do I find the lengths of each side of a rectangular prism, if I'm only given a polynomial for the area?

Question

I have an example question:

The volume of a rectangular prism is 2x² + 13x² + 21x units³, what are the lengths of each side?

I've tried but i just can't figure it out.

Answer 1

Hi Suezanna,

First of all you have a mistake in writing 2x² + 13x² + 21x units³,

because it is volume, so must be 2x3 + 13x² + 21x units³,

Anyway, you know the volume of rectangular prism = height * area of base

SO factor of x in equation of volume 2x3 + 13x² + 21x units³ is necessary

x( 2x^2 + 13x + 21) now you need change to multiple expression

x( 2x + 7 ) ( x + 3 )

As a result x, 2x + 7, x + 3 are the the lengths of each side of prism.

I hope it is useful,

Minoo