Question

Which example correctly demonstrates polynomial subtraction? (1 point)
• (2x2 + 6x + 1) - (3x2 + 3x + 9) = 5x2 + 9x + 10
• (2x" + 6x + 1) - (3x2 + 3x + 9) = -x2 + 3x - 8
• (2x2 + 6x + 1) - (3x2 + 3х + 9) = - 5x2 + 3х - 8
• (2x2 + 6x + 1) - (3x2 + 3x + 9) = x2 + 3x + 8

Answer 1

To determine which example correctly demonstrates polynomial subtraction, we need to perform the subtraction for each case.

The expression is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]

This can be simplified as follows:
1. Distribute the negative sign:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

2. Combine like terms:
- For \(x^2\): \(2x^2 - 3x^2 = -1x^2\)
- For \(x\): \(6x - 3x = 3x\)
- For the constant term: \(1 - 9 = -8\)

So we have:
\[
-1x^2 + 3x - 8 \text{ or } -x^2 + 3x - 8
\]

Now, let's analyze the provided options:

1. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\)
- This is incorrect.

2. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\)
- This is correct.

3. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8\)
- This is incorrect.

4. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8\)
- This is incorrect.

Thus, the correct answer is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]