Which example correctly demonstrates polynomial

To correctly demonstrate polynomial subtraction, we need to subtract each corresponding term in the two polynomials. Let's break down the expression (2x² + 6x + 1) − (3x² + 3x + 9):

1. **Subtracting the \(x^2\) terms:**
\(2x² - 3x² = -1x²\) or \(-x²\)

2. **Subtracting the \(x\) terms:**
\(6x - 3x = 3x\)

3. **Subtracting the constant terms:**
\(1 - 9 = -8\)

Putting it all together, we get:

\((-x² + 3x - 8)\)

Now let's compare this with the given options:

- **First option:** \((2x² + 6x + 1) − (3x² + 3x + 9) = −x² + 3x − 8\) (This is correct)
- **Second option:** \((2x² + 6x + 1) − (3x² + 3x+9) = 5x + 29 + 10\) (This is incorrect)
- **Third option:** \((2x² + 6x + 1) − (3x² + 3x+9) = x² + 3x + 8\) (This is incorrect)
- **Fourth option:** \((2x² + 6x + 1) − (3x² + 3x+9) = -5x² + 3x - 8\) (This is incorrect)

Therefore, the correct example that demonstrates polynomial subtraction is:

**(2x² + 6x + 1) − (3x² + 3x + 9) = −x² + 3x − 8**.