Which example correctly demonstrates polynomial subtraction?(1 point) Responses (2x2+6x+1)−(3x2+3x+9)=−5x2+3x−8 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals 2 x squared plus 6 x plus 1 minus 3 x squared minus 3 x minus 9 (2x2+6x+1)−(3x2+3x+9)=x2+3x+8 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 6 x minus 4 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 4 right parenthesis (2x2+6x+1)−(3x2+3x+9)=−x2+3x−8 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus 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)=5x2+9x+10

To perform polynomial subtraction correctly, we need to subtract each term in the second polynomial from the corresponding term in the first polynomial. Here, we will break down the operation step by step using the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\).

1. Start with the expression:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]

2. Distribute the negative sign through the second polynomial:
\[
2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

3. Now, combine like terms:
- For the \(x^2\) terms: \(2x^2 - 3x^2 = -x^2\)
- For the \(x\) terms: \(6x - 3x = 3x\)
- For the constant terms: \(1 - 9 = -8\)

4. Therefore, the result of the subtraction is:
\[
-x^2 + 3x - 8
\]

Now, looking at the options provided:

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

Thus, the correct demonstration of polynomial subtraction is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]
**The correct response is Response 3.**