Question 936346
w=15, width of rectangle
L=20, length of rectangle
x, side length of square removed from the corners
v, volume of rectangular box formed


x is the single variable, and although v is another single variable, v is also the function for volume which depends on x.


{{{highlight_green(v=(w-2x)(L-2x)x)}}}


The factorized form allows you to find three Real roots for the graph.  Checking for signs of v on the intervals is also best done using the factorized form of the function.


Do you know simple derivatives of polynomials?  If you do, then you can use this to find maximum and minimum points of the graph.  That means, maximum  (and minimum) values for the volume v.  You might use a graphing calculator or other software to check your work.


The graph is not shown for you in this post, but the code for it would be, unless some graph dimensions need adjustment,
graph(300,300,-4,14,-4,14,(15-2x)(20-2x)x)


(the rendering tags simply not included for the graph code).