which example correctly demonstrates polynomial addition

To determine which example correctly demonstrates polynomial addition, we need to add the polynomials \(2x^2 + 6x + 1\) and \(3x^2 + 3x + 9\):

1. **Add the coefficients of \(x^2\):**
- \(2 + 3 = 5\)

2. **Add the coefficients of \(x\):**
- \(6 + 3 = 9\)

3. **Add the constant terms:**
- \(1 + 9 = 10\)

Combining all these results, we get:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]

Thus, the correct example that demonstrates polynomial addition is:
\[
(2x^2+6x+1)+(3x^2+3x+9)=5x^2+9x+10
\]