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)=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)=−x2+3x−8

Answer 1

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

Let's analyze each option:

1. Option 1: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\)

   • Correctly adds: \(2x^2 + 3x^2 = 5x^2\), \(6x + 3x = 9x\), \(1 + 9 = 10\).
   • This option is correct.

2. Option 2: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10\)

   • Incorrect, because \(2x^2 + 3x^2\) cannot result in \(5x^4\). This shows incorrect degree for the \(x\) term.

3. Option 3: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10\)

   • Incorrect, because \(2x^2 + 3x^2\) gives \(5x^2\), not \(13x^2\).

4. Option 4: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8\)

   • Incorrect, as it does not add up correctly; the resulting coefficients do not match.

The correct answer is Option 1: \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\).