Note that I understand the math and was able to solve for the answer. What I really want to know is:

Please see attached question and answer from my Advanced Functions course. Note that I understand the math and was able to solve for the answer.

What I really want to know is:

How is it that solving for the roots of the equation would give us the dimensions of the squares that had to be cut out?

I solved the question because I was able to recognize that I needed to use the factor theorem and long division to solve for x, and if x represents the width of each square, then x must be the W and H of the square, but I can't see/visualize how the formula was derived to work out the volume of the box (832cm^3).

Perhaps the real question is, how was the formula derived?

I could likely answer these types of questions again, but a deeper understanding would enable me to solve much faster, so any help would be much appreciated, thanks!

• Attachment 1
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• Attachment 3