Question

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

(2x2+6x+1)+(3x2+3x+9)=−x2+3x−8
open paren 2 x squared plus 6 x plus 1 close paren plus open paren 3 x squared plus 3 x plus 9 close paren is equal to negative x squared plus 3 x minus 8

(2x2+6x+1)+(3x2+3x+9)=13x2+9x+10
open paren 2 x squared plus 6 x plus 1 close paren plus open paren 3 x squared plus 3 x plus 9 close paren is equal to 13 x squared plus 9 x plus 10

(2x2+6x+1)+(3x2+3x+9)=5x2+9x+10
open paren 2 x squared plus 6 x plus 1 close paren plus open paren 3 x squared plus 3 x plus 9 close paren is equal to 5 x squared plus 9 x plus 10

(2x2+6x+1)+(3x2+3x+9)=5x4+9x2+10

Answer 1

To perform polynomial addition, we need to combine like terms correctly. Let's break down the expression \((2x^2 + 6x + 1) + (3x^2 + 3x + 9)\):

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

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

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

Putting it all together, we have:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]

Now, let's check the response options:

- **Response 1**: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8\) - **Incorrect**

- **Response 2**: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10\) - **Incorrect**

- **Response 3**: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) - **Correct**

- **Response 4**: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10\) - **Incorrect**

Thus, the correct demonstration of polynomial addition is:
**Response 3: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\)**.