Question

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

Answer 1

Consider this option:
if given 2x³+5x²-8x-20 ,then it is possible to make up two groups:
(2x³-8x) and (5x²-20).
2x³+5x²-8x-20=(2x³-8x)+(5x²-20)=2x(x²-4)+5(x²-4)=(x²-4)(2x+5).
Then it is possible to re-write (x²-4) as ((x+2)(x-2)):
(x²-4)(2x+5)=(x+2)(x-2)(2x+5).

answer: (x+2)(x-2)(2x+5)

Answer 2

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

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)