The volume of a rectangular prism is given by the formula (length•width•height). What are the length, width, and height of the prism if the volume is ?

Question

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 1

So, Jada, we need three factors, right?

 

The first thing we can factor out is 3x.

 

3x(x² + 3x + 2)

 

We can then factor the trinomial into two binomials. Hopefully you know how to do that.

 

3x(x + 2)(x + 1)

 

So, our length, width and height are 3x, x + 2 and x + 1.

 

Hope this helps!