What were the dimensions of the original piece of cardboard

Question

I am folding and making a cardboard box with different volumes, with equal sized squares. If x is the length of a side of a small square (in inches), then the volume is V=21x-20x^2+4x^3.

What were the dimensions of the original piece of cardboard. To find the value of x, I factored the equation like this: x(21-20x+4x^2) ==> x(4x^2-20x+21) ==> x(2x-7)(2x-3) I then set both binomials to zero, 2x-7=0 and 2x-3=0, and got x=3.5 and x=1.5. I then drew a sketch of the uncut version of the cardboard and found the dimensions, but for some reason these are incorrect according to the homework. Any ideas on how to solve this problem?

Answer 1

Rewrite the volume as x(7-2x)(3-2x), which would mean that the piece of cardboard originally had dimensions 7" by 3". After building the box, the dimensions would be 7 - 2x by 3 - 2x by x.