# 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?

May 9, 2018

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

#### Explanation:

We can immediately factor out a $3 x$.

$3 x \left(2 {x}^{2} + 9 x - 5\right)$

Let's try and factor the trinomial now.

$3 x \left(2 {x}^{2} + 10 x - x - 5\right)$

$3 x \left(2 x \left(x + 5\right) - \left(x + 5\right)\right)$

$3 x \left(2 x - 1\right) \left(x + 5\right)$

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

Hopefully this helps!