Question

Which example correctly demonstrates polynomial addition?(1 point)
Responses

(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)=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)=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)= 5x4+9x2+10

Answer 1

To correctly demonstrate polynomial addition, we need to correctly combine like terms from the given polynomials.

Let's break down the polynomial addition for:

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

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 have:

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

Thus, the correct response for polynomial addition is:

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

So, the correct choice from your provided options is:

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