1 answer
(click or scroll down)
To perform the polynomial subtraction \( (2x^2 + 6x + 1) - (3x^2 + 3x + 9) \), we need to distribute the negative sign across the second polynomial and then combine like terms.
Let's break it down step by step:
1. Write down the original polynomials:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
2. Distribute the negative sign:
\[
2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
3. Combine 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 get:
\[
-x^2 + 3x - 8
\]
From the provided responses, the correct example that demonstrates polynomial subtraction is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]
So the correct answer is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]