# The volume of a box is 2x^3+9x^2-20x-75 cubic centimeters. Find the length if width is (x+5) centimeters and the height is (x-3) centimeters? Can you please show the work. Thank you

Apr 13, 2017

I got $2 x + 5$

#### Explanation:

Have a look:

Apr 14, 2017

color(red)(2x+5

#### Explanation:

Volume of box$= 2 {x}^{3} + 9 {x}^{2} - 20 x - 75$$c {m}^{3}$ given

Width$= x + 5$ cm given

Height$= x - 3$ cm given

Length?

$\therefore W \times H \times L =$Volume

$\therefore L = \frac{V o l u m e}{W \times H}$

$\therefore W \times H = \left(x - 3\right) \cdot \left(x + 5\right) = {x}^{2} + 2 x - 15$

$\therefore L = \frac{2 {x}^{3} + 9 {x}^{2} - 20 x - 75}{{x}^{2} + 2 x - 15}$

color(white)(000000000000")")underline(color(white)(0000000000000)color(red)(2x+5color(white)(0000))
${x}^{2} + 2 x - 15 \textcolor{w h i t e}{0} \text{)} \textcolor{w h i t e}{0} 2 {x}^{3} + 9 {x}^{2} - 20 x - 75$
$\textcolor{w h i t e}{000000000000 \text{)} 0} \underline{2 {x}^{3} + 4 {x}^{2} - 30 x}$
$\textcolor{w h i t e}{00000000000000000 \text{)} 00} 5 {x}^{2} + 10 x - 75$
$\textcolor{w h i t e}{00000000000000000 \text{)} 00} \underline{5 {x}^{2} + 10 x - 75}$

color(white)(00000")"000)color(red)(2x+5$=$quotient$=$Length