To perform polynomial addition for the given example, we combine like terms from the two polynomials:
- \( (2x^2 + 6x + 1) \)
- \( (3x^2 + 3x + 9) \)
Now, let's add the corresponding terms:
- For \( x^2 \) terms: \( 2x^2 + 3x^2 = 5x^2 \)
- For \( x \) terms: \( 6x + 3x = 9x \)
- For the constant terms: \( 1 + 9 = 10 \)
Putting it all together, we get: \[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \]
So the correct example that demonstrates polynomial addition is:
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10.