To correctly demonstrate polynomial addition, we need to add the corresponding terms of the polynomials together. Let's break it down:
Given polynomials:
- \( (2x² + 6x + 1) \)
- \( (3x² + 3x + 9) \)
Now, we'll add these polynomials term by term:
- For \( x² \) terms: \( 2x² + 3x² = 5x² \)
- For \( x \) terms: \( 6x + 3x = 9x \)
- For constant terms: \( 1 + 9 = 10 \)
Combining these results together, we have: \[ (2x² + 6x + 1) + (3x² + 3x + 9) = 5x² + 9x + 10 \]
Now, we can evaluate the options:
- \((2x² + 6x + 1) + (3x² + 3x + 9) = 13x² + 9x + 10\) (Incorrect)
- \((2x² + 6x + 1) + (3x² + 3x + 9) = 5x² + 9x + 10\) (Correct)
- \((2x² + 6x + 1) + (3x² + 3x + 9) = x² + 3x - 8\) (Incorrect)
- \((2x² + 6x + 1) + (3x² + 3x + 9) = 5x^4 + 9x² + 10\) (Incorrect)
Thus, the correct example that demonstrates polynomial addition is: \[ (2x² + 6x + 1) + (3x² + 3x + 9) = 5x² + 9x + 10 \]