Question

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

A) (2x^2+6x+1)+(3x^2+3x+9)=−x^2+3x−8

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

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

D) (2x^2+6x+1)+(3x^2+3x+9)= 5x^4+9x^2+10

Answer 1

To determine which example correctly demonstrates polynomial addition, we need to perform the addition of the polynomials on the left side of the equation for each option.

Let's evaluate each option:

### A)
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9)
\]
Combine like terms:
- \(2x^2 + 3x^2 = 5x^2\)
- \(6x + 3x = 9x\)
- \(1 + 9 = 10\)

So, this becomes:
\[
5x^2 + 9x + 10
\]
**This is NOT correct because it equals \(5x^2 + 9x + 10\), not \(-x^2 + 3x - 8\).**

### B)
We already calculated the sum in option A, which is \(5x^2 + 9x + 10\).
- This option states \(13x^2 + 9x + 10\).
- This is NOT correct.

### C)
This option also stated:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]
- This one matches our calculation! **This is correct.**

### D)
This option states:
\[
5x^4 + 9x^2 + 10
\]
However, there is no \(x^4\) term in our original polynomials, which makes this option incorrect.

### Conclusion:
The correct response demonstrating polynomial addition is:

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