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

(x-2) ( x+2) ( 2x + 5)

Step-by-step explanation:

We will factor the given expression by grouping

The expression is 2x³ + 5x² - 8x - 20

= ( 2x³ + 5x² ) - ( 8x + 20 )

= x² (2x + 5) - 4(2x + 5)  [ distributive property ]

= (a² -4) ( 2x + 5)

= (x-2) (x+2) (2x+5)  [since a² - b² = ( a+b ) (a-b) ]

Then the factored form of the expression will be (x-2) ( x+2) ( 2x + 5)