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Bot GPT 4-o mini To correctly demonstrate polynomial subtraction, we subtract the corresponding coefficients of like terms in the two polynomials.
Let's perform the subtraction step-by-step for the expression:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
1. Subtract the \(x^2\) terms:
\[
2x^2 - 3x^2 = -1x^2 \quad \text{(or just } -x^2\text{)}
\]
2. Subtract the \(x\) terms:
\[
6x - 3x = 3x
\]
3. Subtract the constant terms:
\[
1 - 9 = -8
\]
Putting it all together, the result of the subtraction is:
\[
-x^2 + 3x - 8
\]
Now, let's match this with the provided options:
1. **Option 1**: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8\) → Incorrect
2. **Option 2**: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\) → Correct!
3. **Option 3**: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) → Incorrect
4. **Option 4**: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8\) → Incorrect
Therefore, the correct answer is **Option 2**:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]