Question

Factor the following polynomial: 6x^3+9x^2+4x+6
(1 point)
Responses

(3x^2+2)(2x+3)
open paren 3 x squared plus 2 close paren times open paren 2 x plus 3 close paren

(2x^2+3)(3x+2)
open paren 2 x squared plus 3 close paren times open paren 3 x plus 2 close paren

(3x^2+6)(2x+1)
open paren 3 x squared plus 6 close paren times open paren 2 x plus 1 close paren

(2x^2+3x)(3x+2)
open paren 2 x squared plus 3 x close paren times open paren 3 x plus 2 close paren
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Answer 1

To factor the polynomial \( 6x^3 + 9x^2 + 4x + 6 \), we can start by grouping the terms:

1. Group the first two terms and the last two terms:
\[
(6x^3 + 9x^2) + (4x + 6)
\]

2. Factor out the greatest common factor from each group:
\[
3x^2(2x + 3) + 2(2x + 3)
\]

3. Now, notice that \( (2x + 3) \) is a common factor:
\[
(3x^2 + 2)(2x + 3)
\]

Therefore, the factored form of the polynomial \( 6x^3 + 9x^2 + 4x + 6 \) is:
\[
(3x^2 + 2)(2x + 3)
\]

Among the provided options, the correct response is:
- (3x^2 + 2)(2x + 3)