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

Answer 1

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.