Question

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

Answer 1

I got `2x+5`

Explanation:

Have a look:

Answer 2

`color(red)(2x+5`

Explanation:

Volume of box`= 2x^3+9x^2-20x-75` `cm^3` given

Width`=x+5` cm given

Height`=x-3` cm given

Length?

`:.W xx H xx L=`Volume

`:.L=(Volume)/(W xx H)`

`:.W xx H=(x-3)*(x+5)=x^2+2x-15`

`:.L=(2x^3+9x^2-20x-75)/(x^2+2x-15)`

`color(white)(000000000000")")underline(color(white)(0000000000000)color(red)(2x+5color(white)(0000))`
`x^2+2x-15color(white)(0)")"color(white)(0)2x^3+9x^2-20x-75`
`color(white)(000000000000")"0)underline(2x^3+4x^2-30x)`
`color(white)(00000000000000000")"00)5x^2+10x-75`
`color(white)(00000000000000000")"00)underline(5x^2+10x-75)`

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