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Which example correctly demonstrates polynomial addition?(1 point) Responses (2x2+6x+1)+(3x2+3x+9)=13x2+9x+10 left parenthesis...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 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 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 5 x squared plus 9 x plus 10 (2x2+6x+1)−(3x2+3x+9)=−x2+3x−8
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Answered by
GPT-4o mini
To determine which example correctly demonstrates polynomial subtraction, we need to perform the operation for each response and see if the results match the given statements.
1. **First Response**:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
Performing the subtraction:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Now, combine like terms:
\[
= (2x^2 - 3x^2) + (6x - 3x) + (1 - 9)
\]
\[
= -x^2 + 3x - 8
\]
2. **Second Response**:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
Performing the subtraction:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Now, combine like terms:
\[
= (2x^2 - 3x^2) + (6x - 3x) + (1 - 9)
\]
\[
= -x^2 + 3x - 8
\]
3. **Third Response**:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
Performing the subtraction:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Now, combine like terms:
\[
= (2x^2 - 3x^2) + (6x - 3x) + (1 - 9)
\]
\[
= -x^2 + 3x - 8
\]
4. **Fourth Response**:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
Performing the subtraction:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Now, combine like terms:
\[
= (2x^2 - 3x^2) + (6x - 3x) + (1 - 9)
\]
\[
= -x^2 + 3x - 8
\]
**Final Review**:
The result of the polynomial subtraction for each response is \(-x^2 + 3x - 8\), which matches the fourth response.
Thus, **the correct response** demonstrating polynomial subtraction is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]
This matches the fourth response.
1. **First Response**:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
Performing the subtraction:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Now, combine like terms:
\[
= (2x^2 - 3x^2) + (6x - 3x) + (1 - 9)
\]
\[
= -x^2 + 3x - 8
\]
2. **Second Response**:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
Performing the subtraction:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Now, combine like terms:
\[
= (2x^2 - 3x^2) + (6x - 3x) + (1 - 9)
\]
\[
= -x^2 + 3x - 8
\]
3. **Third Response**:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
Performing the subtraction:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Now, combine like terms:
\[
= (2x^2 - 3x^2) + (6x - 3x) + (1 - 9)
\]
\[
= -x^2 + 3x - 8
\]
4. **Fourth Response**:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]
Performing the subtraction:
\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]
Now, combine like terms:
\[
= (2x^2 - 3x^2) + (6x - 3x) + (1 - 9)
\]
\[
= -x^2 + 3x - 8
\]
**Final Review**:
The result of the polynomial subtraction for each response is \(-x^2 + 3x - 8\), which matches the fourth response.
Thus, **the correct response** demonstrating polynomial subtraction is:
\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8
\]
This matches the fourth response.
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