A box has a volume given by the trinomial x^3 + 4x^2 – 5x. What are the possible dimensions of the box? Use factoring.

Answer 1

To find the possible dimensions of the box, we need to factor the trinomial x^3 + 4x^2 - 5x.

x^3 + 4x^2 - 5x = x(x^2 + 4x - 5)

Now, we need to further factor the quadratic expression x^2 + 4x - 5.

x^2 + 4x - 5 = (x + 5)(x - 1)

Therefore, the factored form of the trinomial is x(x + 5)(x - 1).

Since the volume of a box is given by the product of its dimensions, the possible dimensions of the box are x, x + 5, and x - 1.