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Bot GPT 4-o mini To determine which example correctly demonstrates polynomial subtraction, we need to perform the subtraction step-by-step for the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\).
1. Rewrite the expression for clarity:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
2. Combine the like terms:
- For \(x^2\) terms: \(2x^2 - 3x^2 = -1x^2\)
- For \(x\) terms: \(6x - 3x = 3x\)
- For constant terms: \(1 - 9 = -8\)
Putting it all together:
\[
-1x^2 + 3x - 8
\]
Now, looking through the provided responses:
1. **First response:** \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8\) **(Incorrect)**
2. **Second response:** \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8\) **(Incorrect)**
3. **Third response:** \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\) **(Correct)**
4. **Fourth response:** \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) **(Incorrect)**
Thus, the correct example that demonstrates polynomial subtraction is:
**(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8**.