Which example correctly demonstrates polynomial addition?(1 point)

Question

Responses

(2x2+6x+1)+(3x2+3x+9)=13x2+9x+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 3 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 6 x plus 9 right parenthesis

(2x2+6x+1)+(3x2+3x+9)=5x2+9x+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus 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)= 5x4+9x2+10
left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x squared plus 3 x plus 9 right parenthesis equals left parenthesis 2 x squared plus 3 x squared right parenthesis plus left parenthesis 6 x plus 3 x right parenthesis plus left parenthesis 1 plus 9 right parenthesis

(2x2+6x+1)+(3x2+3x+9)=−x2+3x−8

Answer 1

To demonstrate polynomial addition correctly, we need to combine like terms properly.

Let's analyze each response:

1. First response: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10\)
   This is incorrect because \(2x^2 + 3x^2\) should equal \(5x^2\), not \(13x^2\).

2. Second response: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\)
   This is correct. We combine like terms:

   • \(2x^2 + 3x^2 = 5x^2\)
   • \(6x + 3x = 9x\)
   • \(1 + 9 = 10\)

3. Third response: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10\)
   This is incorrect because there are no \(x^4\) terms in the original polynomials.

4. Fourth response: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8\)
   This is incorrect because the calculations do not properly add the terms.

The correct example demonstrating polynomial addition is the second response:
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\).