Question

Express the polynomial as a product of linear factors 2x^3+4x^2-2x-4

Answer 1

regroup: (2x³+4x²)-(2x+4)
factor: 2x²(x+2)-2(x+2)
(2x²-2)(x+2)
2(x²-1)(x+2)
2(x+1)(x-1)(x+2) is the final answer.

Answer 2

2(x-1)(x+1)(x+2)

Explanation:

Given :
`2x^3+4x^2-2x-4`

To Find: Express the polynomial as a product of linear factors

Solution:

`2x^3+4x^2-2x-4`

`(2x^3+4x^2)-(2x-4)`

`2x^2(x+2)-2(x+2)`

`(2x^2-2)(x+2)`

`2(x^2-1)(x+2)`

Using identity :
`x^2-a^2=(x-a)(x+a)`

`2(x-1)(x+1)(x+2)`

So,
`2x^3+4x^2-2x-4` as a product of linear factors :

`2x^3+4x^2-2x-4=2(x-1)(x+1)(x+2)`