# The dimensions for a rectangular prism are x+2 for the length, x +3 for the width, and x for the height. What the volume of the prism expressed as a polynomial in standard form?

Mar 26, 2017

${x}^{3} + 5 {x}^{2} + 6 x$

#### Explanation:

The volume of a rectangular prism is given by the formula $V = l w h$ where $V$ is the volume, $l$ is the length, $w$ is the width, and $h$ is the height.

For this rectangular prism, $V = \left(x + 2\right) \left(x + 3\right) \left(x\right)$. To put it in standard form it must be multiplied out. $V = \left({x}^{2} + 5 x + 6\right) x = {x}^{3} + 5 {x}^{2} + 6 x$

Mar 27, 2017

${x}^{3} + 5 {x}^{2} + 6 x$

#### Explanation:

We know all the dimensions of the rectangular prism. We need to find its volume

color(blue)("volume"=lwh

Whers, $l , w \mathmr{and} h$ are length,width and height

So,

$\rightarrow \left(x + 2\right) \left(x + 3\right) \left(x\right)$

Multiply $\left(x + 2\right) \mathmr{and} \left(x + 3\right)$ using the foil method

$\rightarrow x \left({x}^{2} + 5 x + 6\right)$

color(green)(rarrx^3+5x^2+6x

It is already in the standard form (in decreasing powers)

Hope this helps....! :)