Question

Which example correctly demonstrates polynomial addition?(1 point)

(2x^2+6x+1)+(3x^2+3x+9)=−x^2+3x−8

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

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

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

Answer 1

To demonstrate polynomial addition, we need to combine the like terms from both polynomials correctly. Let's add the given polynomials step by step.

The two polynomials we are adding are:
1. \( 2x^2 + 6x + 1 \)
2. \( 3x^2 + 3x + 9 \)

Now, adding the like terms:
- For \(x^2\) terms: \(2x^2 + 3x^2 = 5x^2\)
- For \(x\) terms: \(6x + 3x = 9x\)
- For the constant terms: \(1 + 9 = 10\)

So, the sum is:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]

Thus, the correct answer that demonstrates polynomial addition is:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]

So the correct option is:
**(2x^2+6x+1)+(3x^2+3x+9)=5x^2+9x+10**.