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)=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)=−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

Answer 1

Let's perform the polynomial subtraction for the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\).

1. Start with the original expression: \[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) \]

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

3. Combine like terms:

   • For the \(x^2\) terms: \(2x^2 - 3x^2 = -1x^2\) or \(-x^2\)
   • For the \(x\) terms: \(6x - 3x = 3x\)
   • For the constant terms: \(1 - 9 = -8\)

4. Putting it all together: \[ -x^2 + 3x - 8 \]

This simplifies to: \[ -x^2 + 3x - 8 \]

Thus, the correct example demonstrating polynomial subtraction is:

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

So the first response is correct: \[ \text{(2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8} \]