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

Answer:

To factor 2x^3 + 5x^2 – 8x – 20, first check for a greatest common factor. Since there isn't one for all terms, factor by grouping. Group the first two terms and the last two terms: (2x^3 + 5x^2) + (– 8x – 20). Factor out x^2 from the first group and -4 from the second group to get x^2(2x + 5) - 4(2x + 5). This simplifies to (x^2 - 4)(2x + 5). Finally, factor the difference of squares (x^2 - 4) into (x - 2)(x + 2). The completely factored form is (2x + 5)(x + 2)(x - 2).