Question

Which example correctly demonstrates polynomial addition?(1 point) Responses (2x2+6x+1)+(3x2+3x+9)= 5x4+9x2+10 left parenthesis 2 x squared plus 6 x plus 1 right parenthesis plus left parenthesis 3 x .

Answer 1

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

Let's analyze the example given:

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

1. **Identify like terms**:
- For \(x^2\) terms: \(2x^2\) and \(3x^2\).
- For \(x\) terms: \(6x\) and \(3x\).
- For constant terms: \(1\) and \(9\).

2. **Combine the like terms**:
- \(2x^2 + 3x^2 = 5x^2\)
- \(6x + 3x = 9x\)
- \(1 + 9 = 10\)

3. **Combine the results**:
- So, \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\).

Therefore, the correct representation of polynomial addition is:

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

The given expression in the first part did not represent the correct sum of the polynomials since it incorrectly led to \(5x^4\) which is not a term present in either polynomial.