Question

Which example correctly demonstrates polynomial subtraction?(1 point) Responses (2x2+6x+1)−(3x2+3x+9)=−x2+3x−8 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals negative x squared plus 3 x minus 8 (2x2+6x+1)−(3x2+3x+9)=x2+3x+8 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 6 x minus 4 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 4 right parenthesis (2x2+6x+1)−(3x2+3x+9)=−5x2+3x−8 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis minus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals 2 x squared plus 6 x plus 1 minus 3 x squared minus 3 x minus 9 (2x2+6x+1)−(3x2+3x+9)=5x2+9x+10

Answer 1

To determine which example correctly demonstrates polynomial subtraction, let's perform the subtraction for the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\).

1. **Write the expression down**:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]

2. **Distribute the negative sign across the second polynomial**:
\[
2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

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 have:
\[
-x^2 + 3x - 8
\]

Now, let's evaluate the given responses:

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

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

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

4. **Response 4**:
\((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) **(This is incorrect)**

The correct answer is **Response 1**: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\).