Which example correctly demonstrates polynomial addition?

To demonstrate polynomial addition correctly, we need to add the like terms from the two polynomials:

Given polynomials:

\[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) \]

Now, let's add the coefficients of like terms:

1. For \(x^2\) terms:
\(2x^2 + 3x^2 = 5x^2\)

2. For \(x\) terms:
\(6x + 3x = 9x\)

3. For constant terms:
\(1 + 9 = 10\)

Putting these together:

\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]

Now, we check the options provided:

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

Thus, the correct example that demonstrates polynomial addition is:

**D.** \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\)