To perform polynomial subtraction, we need to distribute the negative sign to the terms in the second polynomial before combining like terms.
Let's subtract the polynomials step by step:
\[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) \]
Distributing the negative sign gives us:
\[ 2x^2 + 6x + 1 - 3x^2 - 3x - 9 \]
Now, we combine the like terms:
- For \(x^2\) terms: \(2x^2 - 3x^2 = -1x^2\) or \(-x^2\)
- For \(x\) terms: \(6x - 3x = 3x\)
- For constant terms: \(1 - 9 = -8\)
Putting it all together, we find:
\[ -x^2 + 3x - 8 \]
Thus, the correct answer is:
D. (2x^2 + 6x + 1) – (3x^2 + 3x + 9) = -x^2 + 3x – 8.