Question

Factor completely 2x3 + 4x2 + 6x + 12.

2(x3 + 2x2 + 3x + 6)
(2x2 + 6)(x + 2)
2[(x2 + 2)(x + 3)]
2[(x2 + 3)(x + 2)]

Answer 1

2x^2(x+2) +6(x+2) = (2x^2 +6)(x+2) = 2(x^2 +3)(x+2)

so this mean that the 4th choice will be right sure

Answer 2

`2[(x^2+ 3)(x + 2)]`

Explanation:

Given :
`2x^3 + 4x^2 + 6x + 12`

To Find: factor Completely

Solution:

`2(x^3 + 2x^2 + 3x + 6)`

Taking 2 as common

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

Now factorizing further

`2[(x^2+ 3)(x + 2)]`

So, the factored form of
`2x^3 + 4x^2 + 6x + 12` is
`2[(x^2+ 3)(x + 2)]`

Hence Option D is correct.