To determine which example correctly demonstrates polynomial addition, we need to perform the addition of the polynomials on the left side of the equation for each option.
Let's evaluate each option:
A)
\[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) \] Combine like terms:
- \(2x^2 + 3x^2 = 5x^2\)
- \(6x + 3x = 9x\)
- \(1 + 9 = 10\)
So, this becomes: \[ 5x^2 + 9x + 10 \] This is NOT correct because it equals \(5x^2 + 9x + 10\), not \(-x^2 + 3x - 8\).
B)
We already calculated the sum in option A, which is \(5x^2 + 9x + 10\).
- This option states \(13x^2 + 9x + 10\).
- This is NOT correct.
C)
This option also stated: \[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \]
- This one matches our calculation! This is correct.
D)
This option states: \[ 5x^4 + 9x^2 + 10 \] However, there is no \(x^4\) term in our original polynomials, which makes this option incorrect.
Conclusion:
The correct response demonstrating polynomial addition is:
C) (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10.