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

Answer:

First check for a greatest common factor. Then factor by grouping: x^2(2x + 5) - 4(2x + 5) = (2x + 5)(x^2 - 4). Recognize x^2 - 4 as a difference of squares and factor completely: (2x + 5)(x + 2)(x - 2).