Which example correctly demonstrates polynomial subtraction?(1 point)

Question

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)=−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)=5x2+9x+10

Answer 1

To determine which example correctly demonstrates polynomial subtraction, we need to perform the subtraction \( (2x^2 + 6x + 1) - (3x^2 + 3x + 9) \).

1. Rewrite the subtraction: \[ 2x^2 + 6x + 1 - (3x^2 + 3x + 9) \] This is the same as: \[ 2x^2 + 6x + 1 - 3x^2 - 3x - 9 \]

2. Combine like terms:

   • For \( x^2 \): \[ 2x^2 - 3x^2 = -1x^2 \text{ or } -x^2 \]
   • For \( x \): \[ 6x - 3x = 3x \]
   • For the constant term: \[ 1 - 9 = -8 \]

Putting it all together, we get: \[ -x^2 + 3x - 8 \]

Now, let's evaluate the given responses:

1. Response 1: \( (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8 \) (Incorrect)

2. Response 2: \( (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8 \) (Incorrect)

3. Response 3: \( (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8 \) (Correct)

4. Response 4: \( (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \) (Incorrect)

Therefore, the correct response is:

Response 3: (2x² + 6x + 1) − (3x² + 3x + 9) = −x² + 3x − 8.