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Use the given volume of a box and its length and width to express the height of the box algebraically. (Simplify your answer completely.)

Volume is 

10x^3 + 47x^2 + 16x − 48,

 length is 

5x − 4,

 width is 

2x + 3

Guest Oct 14, 2018
 #1
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V  =  L  * W  * H ...so...

 

10x^3  + 47x^2  + 16x - 48  = [ 5x - 4] [ 2x + 3] * H

 

10x^3 + 47x^2  + 16x  - 48 =  [ 10x^2 - 8x + 15x -12 ] * H

 

10x^3 + 47x^2 + 16x  - 48 =  [ 10x^2 + 7x -12 ] * H

 

We can find the height by  dividing both sides by  [10x^2 + 7x -12] 

 

So

 

H  =   [10x^3 + 47x^2 + 16x  -48]  / [ 10x^2 + 7x  - 12 ]

 

Performing ploynomial division to find the height , we have

 

 

                                  x   +  4

10x^2  +  7x  - 12  [   10x^3  + 47x^2 + 16x  - 48 ]

                                   10x^3 +  7x^2  -12x

                                  ______________________

                                                  40x^2  + 28x  - 48

                                                  40x^2  + 28x  - 48

                                                  _________________

 

So...the height  =    [ x + 4 ]

 

 

 

cool cool cool

CPhill  Oct 15, 2018
edited by CPhill  Oct 15, 2018
edited by CPhill  Oct 15, 2018

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