1 answer
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To find the correct polynomial subtraction, we need to subtract the second polynomial from the first polynomial step by step.
Let's perform the subtraction:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
Distributing the negative sign across the second polynomial yields:
\[
2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Now, we combine like terms:
1. For \(x^2\) terms: \(2x^2 - 3x^2 = -x^2\)
2. For \(x\) terms: \(6x - 3x = 3x\)
3. For constant terms: \(1 - 9 = -8\)
Putting it all together, we have:
\[
-x^2 + 3x - 8
\]
Therefore, the correct response that demonstrates polynomial subtraction is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]
This matches the option:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]