Question

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

Answer 1

To perform the polynomial subtraction \( (2x^2 + 6x + 1) - (3x^2 + 3x + 9) \), we need to distribute the negative sign across the second polynomial and then combine like terms.

Let's break it down step by step:

1. Write down the original polynomials: \[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) \]

2. Distribute the negative sign: \[ 2x^2 + 6x + 1 - 3x^2 - 3x - 9 \]

3. Combine like terms:

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

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

From the provided responses, the correct example that demonstrates polynomial subtraction is: \[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8 \]

So the correct answer is: \[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8 \]