Which example correctly demonstrates polynomial addition?

To determine which example correctly demonstrates polynomial addition, let's perform the addition for each option:

1. **A)**
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9)
\]
Combining like terms:
\[
(2x^2 + 3x^2) + (6x + 3x) + (1 + 9) = 5x^2 + 9x + 10
\]
This statement is correct.

2. **B)**
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9)
\]
Combining like terms again:
\[
(2x^2 + 3x^2) + (6x + 3x) + (1 + 9) = 5x^2 + 9x + 10
\]
However, B states it equals \( 5x^4 + 9x^2 + 10 \), which is incorrect.

3. **C)**
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9)
\]
Again, combining like terms:
\[
5x^2 + 9x + 10
\]
But C states it equals \( 13x^2 + 9x + 10 \), which is also incorrect.

4. **D)**
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9)
\]
Combining the like terms:
\[
5x^2 + 9x + 10
\]
However, D claims it equals \( -x^2 + 3x - 8 \), which is incorrect as well.

Thus, the only option that correctly demonstrates polynomial addition is **A)**:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]