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

The polynomial may have solutions which are the divisors of -20, therefore -20 has the following divisors: .
If x=1, then ,
if x=-1, then ,
if x=2, then , then x=2 is a solution and you have the first factor (x-2). 
If x=-2, then , then x=-2 is a solution, so you have the second factor (x+2).
Since x-2 and x+2 are two factors of , then the polynomial is a divisor of and dividing the polynomial  by you obtain 
 .

You have the polynomial 2x³+5x²-8x-20=0
 To factor you must apply the steps shown below:
 1. Form two groups and factor the Greatest Common Factor of both groups, which are x² and 4
 x²(2x+5)-4(2x+5)=0
 2. Combine both groups to obtain a monomial:
 (x²-4)(2x+5)=0
 3. Factor (x²-4) by Difference of squares:
 (x-2)(x+2)(2x+5)=0
 4. Then you obtain the following result:
 x=2
 x=-2
 x=-5/2 
 It can be factor by using the Greatest Common Factor and the Difference of squares.