Question

Which example correctly demonstrates polynomial addition?(1 point)
Responses

(2x2+6x+1)+(3x2+3x+9)= 5x4+9x2+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 3 x squared right parenthesis plus left parenthesis 6 x plus 3 x right parenthesis plus left parenthesis 1 plus 9 right parenthesis

(2x2+6x+1)+(3x2+3x+9)=5x2+9x+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals 5 x squared plus 9 x plus 10

(2x2+6x+1)+(3x2+3x+9)=13x2+9x+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 3 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 6 x plus 9 right parenthesis

(2x2+6x+1)+(3x2+3x+9)=−x2+3x−8

Answer 1

To determine which example correctly demonstrates polynomial addition, we need to correctly add the two polynomials:

\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9)
\]

Let's combine the like terms:

1. **Combine \(x^2\) terms:**
\[
2x^2 + 3x^2 = 5x^2
\]

2. **Combine \(x\) terms:**
\[
6x + 3x = 9x
\]

3. **Combine constant terms:**
\[
1 + 9 = 10
\]

So, the sum of the two polynomials is:

\[
5x^2 + 9x + 10
\]

Now, comparing the responses:

1. The first option gives \(5x^4 + 9x^2 + 10\), which is incorrect.
2. The second option gives \(5x^2 + 9x + 10\), which is correct.
3. The third option gives \(13x^2 + 9x + 10\), which is incorrect.
4. The fourth option gives \(-x^2 + 3x - 8\), which is incorrect.

The correct response demonstrating polynomial addition is:

**(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10**.