Question
Factor the following polynomial: 6x3+9x2+4x+6 (1 point) Responses (3x2+2)(2x+3) open paren 3 x squared plus 2 close paren times open paren 2 x plus 3 close paren (2x2+3)(3x+2) open paren 2 x squared plus 3 close paren times open paren 3 x plus 2 close paren (3x2+6)(2x+1) open paren 3 x squared plus 6 close paren times open paren 2 x plus 1 close paren (2x2+3x)(3x+2)
Answers
GPT-4o mini
To factor the polynomial \(6x^3 + 9x^2 + 4x + 6\), we can start by grouping the terms to see if we can factor by grouping.
First, let's rewrite the polynomial:
\[
6x^3 + 9x^2 + 4x + 6
\]
We can group the first two terms and the last two terms:
\[
(6x^3 + 9x^2) + (4x + 6)
\]
Now we can factor out the common factors in each group:
1. From the first group, \(6x^3 + 9x^2\), we can factor out \(3x^2\):
\[
3x^2(2x + 3)
\]
2. From the second group, \(4x + 6\), we can factor out \(2\):
\[
2(2x + 3)
\]
Now we have:
\[
3x^2(2x + 3) + 2(2x + 3)
\]
Notice that \(2x + 3\) is common in both terms, so we can factor it out:
\[
(2x + 3)(3x^2 + 2)
\]
Thus, the factored form of the polynomial \(6x^3 + 9x^2 + 4x + 6\) is:
\[
(2x + 3)(3x^2 + 2)
\]
This matches the response label:
**(2x + 3)(3x^2 + 2)**.
So, the answer is:
\((2x + 3)(3x + 2)\)
First, let's rewrite the polynomial:
\[
6x^3 + 9x^2 + 4x + 6
\]
We can group the first two terms and the last two terms:
\[
(6x^3 + 9x^2) + (4x + 6)
\]
Now we can factor out the common factors in each group:
1. From the first group, \(6x^3 + 9x^2\), we can factor out \(3x^2\):
\[
3x^2(2x + 3)
\]
2. From the second group, \(4x + 6\), we can factor out \(2\):
\[
2(2x + 3)
\]
Now we have:
\[
3x^2(2x + 3) + 2(2x + 3)
\]
Notice that \(2x + 3\) is common in both terms, so we can factor it out:
\[
(2x + 3)(3x^2 + 2)
\]
Thus, the factored form of the polynomial \(6x^3 + 9x^2 + 4x + 6\) is:
\[
(2x + 3)(3x^2 + 2)
\]
This matches the response label:
**(2x + 3)(3x^2 + 2)**.
So, the answer is:
\((2x + 3)(3x + 2)\)