Question

Which example correctly demonstrates polynomial addition?(1 point) 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)=−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)= 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)=5x2+9x+10

Answer 1

To perform polynomial addition correctly, we need to combine like terms from both polynomials. Here we have the two polynomials:

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

Let's add these two polynomials step by step:

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:

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

Thus, the correct example demonstrating polynomial addition is:

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