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Which example correctly demonstrates polynomial subtraction?(1 point) Responses (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 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)=−x2+3x−8

1 answer

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

Let's perform the calculation step-by-step:

  1. Start with the first polynomial: \[ 2x^2 + 6x + 1 \]

  2. Subtract the second polynomial: \[ -(3x^2 + 3x + 9) = -3x^2 - 3x - 9 \]

  3. Combine the two results: \[ (2x^2 + 6x + 1) + (-3x^2 - 3x - 9) = 2x^2 - 3x^2 + 6x - 3x + 1 - 9 \]

  4. Simplifying each term:

    • \(2x^2 - 3x^2 = -x^2\)
    • \(6x - 3x = 3x\)
    • \(1 - 9 = -8\)

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

Now we can check which of the provided responses matches this result:

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

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

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

  4. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\) (This is correct.)

Therefore, the fourth response correctly demonstrates polynomial subtraction.