Question

Which example correctly demonstrates polynomial
addition? (1 point)
(2x² + 6x + 1) + (3x² + 3x+9) = 13x² + 9x + 10
(2x² + 6x + 1) + (3x² + 3x+9) = 5x² + 9x + 10
(2x² + 6x + 1) + (3x² + 3x+9)= = x² + 3x - 8
(2x² + 6x + 1) + (3x² + 3x+9) = 5x4 +9x² + 10

Answer 1

To correctly demonstrate polynomial addition, we need to add the corresponding terms of the polynomials together. Let's break it down:

Given polynomials:
- \( (2x² + 6x + 1) \)
- \( (3x² + 3x + 9) \)

Now, we'll add these polynomials term by term:

1. For \( x² \) terms: \( 2x² + 3x² = 5x² \)
2. For \( x \) terms: \( 6x + 3x = 9x \)
3. For constant terms: \( 1 + 9 = 10 \)

Combining these results together, we have:
\[
(2x² + 6x + 1) + (3x² + 3x + 9) = 5x² + 9x + 10
\]

Now, we can evaluate the options:

1. \((2x² + 6x + 1) + (3x² + 3x + 9) = 13x² + 9x + 10\) **(Incorrect)**
2. \((2x² + 6x + 1) + (3x² + 3x + 9) = 5x² + 9x + 10\) **(Correct)**
3. \((2x² + 6x + 1) + (3x² + 3x + 9) = x² + 3x - 8\) **(Incorrect)**
4. \((2x² + 6x + 1) + (3x² + 3x + 9) = 5x^4 + 9x² + 10\) **(Incorrect)**

Thus, the correct example that demonstrates polynomial addition is:
\[
(2x² + 6x + 1) + (3x² + 3x + 9) = 5x² + 9x + 10
\]