# The volume of a right rectangular prism is expressed by V(x) = x^3+2x^2-x-2. What could the dimensions of the prism be?

Jul 11, 2015

$V \left(x\right) = {x}^{3} + 2 {x}^{2} - x - 2 = \left(x - 1\right) \left(x + 1\right) \left(x + 2\right)$

So the dimensions could be $\left(x - 1\right) \times \left(x + 1\right) \times \left(x + 2\right)$

#### Explanation:

Factor by grouping

$V \left(x\right) = {x}^{3} + 2 {x}^{2} - x - 2$

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

$= {x}^{2} \cdot \left(x + 2\right) - 1 \cdot \left(x + 2\right)$

$= \left({x}^{2} - 1\right) \left(x + 2\right)$

$= \left({x}^{2} - {1}^{2}\right) \left(x + 2\right)$

$= \left(x - 1\right) \left(x + 1\right) \left(x + 2\right)$

...using the difference of squares identity:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$