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To correctly perform polynomial subtraction, we need to carefully distribute the negative sign and combine like terms.
Let's evaluate the expression step by step:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
This can be rewritten as:
\[
2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Now, let's combine the like terms:
- For the \(x^2\) terms: \(2x^2 - 3x^2 = -1x^2\) or \(-x^2\)
- For the \(x\) terms: \(6x - 3x = 3x\)
- For the constant terms: \(1 - 9 = -8\)
Putting it all together, we have:
\[
-x^2 + 3x - 8
\]
Thus, the correct answer for the polynomial subtraction is:
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\)
Therefore, the correct response is:
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\).