Question

A box in the shape of a rectangular prism has a volume of `6x^3+27x^2-15x`. What are the dimensions of the box?

Answer 1

The box measures `3x` by `2x- 1` by `x + 5`.

Explanation:

We can immediately factor out a `3x`.

`3x(2x^2 + 9x - 5)`

Let's try and factor the trinomial now.

`3x(2x^2 + 10x - x - 5)`

`3x(2x(x + 5) - (x + 5))`

`3x(2x - 1)(x + 5)`

Therefore, the box measures `3x` by `2x- 1` by `x + 5`.

Hopefully this helps!