Question

Describe the steps you would use to factor 2x^3 + 5x^2 – 8x – 20 completely. Then state the factored form.

Answer 1

To factor 2x^3 + 5x^2 - 8x - 20 completely, you can use the grouping method. The factored form is 2(x + 2)(x^2 - 2).

Step-by-step explanation:

To factor the expression 2x^3 + 5x^2 - 8x - 20, we can use a method called grouping. Here are the steps:

1. Group the terms: (2x^3 + 5x^2) - (8x + 20)
2. Factor out the greatest common factor from each group:
   2x^2(x + 2) - 4(x + 5)
3. Now, we can see that both groups have a common factor of (x + 2), so we can factor that out:
   (x + 2)(2x^2 - 4)
4. Simplify the expression if possible:
   (x + 2)(2x^2 - 4) = 2(x + 2)(x^2 - 2)