Question

can someone show me how to do this? :

3. Bricks are delivered to a work site and stacked in rows and columns, forming a rectangular prism. The length of the prism is 1 foot greater than its width, and its height is 2 feet less than its width. Find the dimensions of the prism formed by the bricks, given that its volume is 40 cubic feet.

Answer 1

w(w^2-w-2)-40=0
Solving that is faster if you know synthetic division. You would use the idea of the Rational Roots Theorem to find values for w to satisfy the cubic equation. I'd suggest first working with +/-4, +/-5, +/-8, +/-10. When you get just one first root, the next two will be easy.

Some further work:
Good News! I tried some long divisions and found +5 or -5 are not roots, but that +4 is a root. One of the binomials is (w-4). The quotient from this was w%5E2%2B3w%2B10. So this means your polynomial equation is
%28w-4%29%28w%5E2%2B3w%2B10%29=0, so the quadratic part should be much easier to manage.
NOTE: The discriminant for that quadratic is -31, so the solution will contain an imaginary part. The only reasonable value for w is 4.

Answer 2

Medal?