Algebra Application Problem

If we cut  2 inch squares form the corners, the dimensions  of the box will be

Length  = ( x - 4) 

Width  = ( x + 2  - 4)    =  ( x  - 2)

Height   = x

So

Length  * Width  * Height  =  96

(x - 4) ( x - 2)  (x)   = 96      simplify

(x^2 - 6x + 8)(x)  = 96

x^3 - 6x^2 + 8x  = 96

x^3 - 6x^2 +  8x  - 96  = 0  

We can solve this with a graph  :

https://www.desmos.com/calculator/iopnxaxlca

The x value that make the above function  =  0  is ≈   6.87  in

So....the  approximate dimensions  of the box  (in inches) are

(6.87 - 4)  ( 6.87  - 2) (6.87)  =

(2.87) ( 4.87) (6.87)