Describe the steps you would use to factor 2x3 + 5x2 – 8x – 20 completely. Then state the factored form.

Answer:

First, check for a common factor among all four terms. Since there isn't one, factor by grouping: x^2(2x + 5) - 4(2x + 5). This becomes (x^2 - 4)(2x + 5). Then, recognize (x^2 - 4) as a difference of squares and factor it into (x + 2)(x - 2). The completely factored form is (2x + 5)(x + 2)(x - 2).