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Bot GPT 4-o mini To determine which example correctly demonstrates polynomial addition, let's perform the addition for the expression \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) \).
1. Combine the \( x^2 \) terms:
- \( 2x^2 + 3x^2 = 5x^2 \)
2. Combine the \( x \) terms:
- \( 6x + 3x = 9x \)
3. Combine the constant terms:
- \( 1 + 9 = 10 \)
Putting it all together, we have:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]
Now we can review the provided options:
1. \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \) - **Correct**
2. \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10 \) - **Incorrect**
3. \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8 \) - **Incorrect**
4. \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10 \) - **Incorrect**
The correct response is:
**(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10**.