Which example correctly demonstrates polynomial addition?(1 point)

Question

Responses

(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
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 negative x squared plus 3 x minus 8

(2x2+6x+1)+(3x2+3x+9)=13x2+9x+10

Answer 1

To correctly demonstrate polynomial addition, we need to add the coefficients of like terms from both polynomials.

Let's perform the addition step-by-step for the expression \((2x^2 + 6x + 1) + (3x^2 + 3x + 9)\):

1. Combine the \(x^2\) terms:
   \(2x^2 + 3x^2 = 5x^2\)

2. Combine the \(x\) terms:
   \(6x + 3x = 9x\)

3. Combine the constant terms:
   \(1 + 9 = 10\)

Putting it all together, we get: \[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10 \]

Now, let's evaluate the responses:

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

2. \((2x^2+6x+1)+(3x^2+3x+9)= 5x^4+9x^2+10\) - This is incorrect; the degree is wrong.

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

4. \((2x^2+6x+1)+(3x^2+3x+9)=13x^2+9x+10\) - This is incorrect; the \(x^2\) term is wrong.

Therefore, the first response is the only example that correctly demonstrates polynomial addition.