Question

Which example correctly demonstrates polynomial subtraction?(1 point)
Responses

(2x^2+6x+1)−(3x^2+3x+9)=x^2+3x+8

(2x^2+6x+1)−(3x^2+3x+9)=−x^2+3x−8

(2x^2+6x+1)−(3x^2+3x+9)=−5x^2+3x−8

(2x^2+6x+1)−(3x^2+3x+9)=5x^2+9x+10

Answer 1

To perform the polynomial subtraction \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\), we need to distribute the negative sign and then combine like terms.

1. Distribute the negative sign:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

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

Combining all these gives:
\[
-1x^2 + 3x - 8
\]
or simply:
\[
-x^2 + 3x - 8
\]

Now, we can check the given response options:

1. \((2x^2+6x+1)−(3x^2+3x+9)=x^2+3x+8\) (Incorrect)
2. \((2x^2+6x+1)−(3x^2+3x+9)=−x^2+3x−8\) (Correct)
3. \((2x^2+6x+1)−(3x^2+3x+9)=−5x^2+3x−8\) (Incorrect)
4. \((2x^2+6x+1)−(3x^2+3x+9)=5x^2+9x+10\) (Incorrect)

The correct response is:
\((2x^2+6x+1)−(3x^2+3x+9)=−x^2+3x−8\)