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Bot GPT 4-o mini To correctly demonstrate polynomial addition, we need to add the like terms of the given polynomials. Let's look at the addition in choice C:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9)
\]
Now, we'll combine the like terms:
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 get:
\[
5x^2 + 9x + 10
\]
Now we can compare this result with each option:
- **A.** \(5x^2 + 9x + 10\) (Correct, but this is a subtraction statement, not an addition).
- **B.** \(-5x^2 + 3x + 8\) (Incorrect).
- **C.** \(x^2 + 3x + 8\) (Incorrect).
- **D.** \(-x^2 + 3x - 8\) (Incorrect).
The correct demonstration of polynomial addition is NOT listed among the choices provided. However, the accurately computed addition is \(5x^2 + 9x + 10\) as shown from the correct calculation steps.
Thus, the answer based solely on polynomial addition should be \(5x^2 + 9x + 10\) but note that none of the choices were correct in demonstrating that operation directly.
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