If the length of a rectangle is x-2 and its area is 2x3 - 8x2 + 2x+12, it's width would be what?

Width would have to be a quadratic

Use long division to find the other factor of the cubic polynomial P (x).

P (x) factors in case it is reducible over R[x]

if it weren't then P (x) mod R [x] would be a field

otherwise you could use the Eisenstein Criterion.