Question

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

(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)= 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)=−x2+3x−8
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 negative x squared plus 3 x minus 8

(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

Answer 1

To determine which example correctly demonstrates polynomial addition, let's perform the addition for 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 we can review the provided options:

1. \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \) - **Correct**
2. \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10 \) - **Incorrect**
3. \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8 \) - **Incorrect**
4. \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10 \) - **Incorrect**

The correct response is:
**(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10**.