Abox has a volume given by the trinomial x^3 + 5x^2 -24x what are the possible dimensions of the box?

Since the volume of a box is just three factors, each being the sides multiplied together, we basically need to factor these into three numbers that would multiply back out and get x^3 + 5x^2 -24x. Factor out an x and get x(x^2+5x-24), then factor normally and get x(x+8)(x-3). (8 and -3 multiply into -24, and add into 5) Your three dimensions are x, x+8, and x-3.