Question

Which example correctly demonstrates polynomial addition?

A, (2x^2+6x+1) + (3x^2+3x+9)=-x^2+3x-8

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

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

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

Answer 1

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

Let's compute \( (2x^2 + 6x + 1) + (3x^2 + 3x + 9) \):

1. **Add the \(x^2\) terms**:
\( 2x^2 + 3x^2 = 5x^2 \)

2. **Add the \(x\) terms**:
\( 6x + 3x = 9x \)

3. **Add the constant terms**:
\( 1 + 9 = 10 \)

Putting this together, we have:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]

Thus, the correct answer is **D**, which shows the correct result of the polynomial addition:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]