Question

Which example correctly demonstrates polynomial addition?(1 point) Responses \left(2x^2+6x+1\right)+\left(3x^2+3x+9\right)=\ 5x^4+9x^2+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 \left(2x^2+6x+1\right)+\left(3x^2+3x+9\right)=13x^2+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 \left(2x^2+6x+1\right)+\left(3x^2+3x+9\right)=-x^2+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 \left(2x^2+6x+1\right)+\left(3x^2+3x+9\right)=5x^2+9x+10

Answer 1

The correct example that demonstrates polynomial addition is:

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

Here's how the addition works 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: \(1 + 9 = 10\).

So the resulting polynomial is \(5x^2 + 9x + 10\). All the other options provided contain incorrect results for polynomial addition.