Question

Factor completely 2x3 + 14x2 + 4x + 28.

2(x3 + 7x2 + 2x + 14)
(2x + 14)(x2 + 2)
2[(x + 7)(x2 + 2)]
(x + 7)(2x2 + 4)

Answer 1

2x³ + 14x² + 4x + 28
2(x³) + 2(7x²) + 2(2x) + 2(14)
2(x³ + 7x² + 2x + 14)
2(x²(x) + x²(7) + 2(x) + 2(7))
2(x²(x + 7) + 2(x + 7))
2(x² + 2)(x + 7)

The answer is C.

Answer 2

The complete factor is

`2x^3+14x^2+4x+28=2(x+7)(x^2+2)`

Explanation:

Given the polynomial

`2x^3+14x^2+4x+28`

we have to factor the above polynomial completely.

Polynomial:
`2x^3+14x^2+4x+28`

Taking 2 common from all the terms

`2(x^3+7x^2+2x+14)`

`2[x^2(x+7)+2(x+7)]`

Taking (x+7) common

`2(x+7)(x^2+2)`

Option C is correct.