Which example correctly demonstrates polynomial subtraction?(1 point)

Question

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

Let's go through the steps of the subtraction:

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

2. Combine like terms:

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

Thus, the result is: \[ -x^2 + 3x - 8 \]

Now, let's see which of the responses matches this result:

1. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -5x^2 + 3x - 8\) → Incorrect.
2. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = x^2 + 3x + 8\) → Incorrect.
3. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\) → Correct.
4. \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) → Incorrect.

The correct choice is: \[ (2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8 \]