1 answer
(click or scroll down)
Bot GPT 4-o mini To correctly demonstrate polynomial addition, we need to add the corresponding coefficients of like terms.
Let's analyze each option:
1. **Option 1:**
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\)
- Correctly adds: \(2x^2 + 3x^2 = 5x^2\), \(6x + 3x = 9x\), \(1 + 9 = 10\).
- This option is correct.
2. **Option 2:**
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10\)
- Incorrect, because \(2x^2 + 3x^2\) cannot result in \(5x^4\). This shows incorrect degree for the \(x\) term.
3. **Option 3:**
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10\)
- Incorrect, because \(2x^2 + 3x^2\) gives \(5x^2\), not \(13x^2\).
4. **Option 4:**
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8\)
- Incorrect, as it does not add up correctly; the resulting coefficients do not match.
The correct answer is **Option 1**:
\((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\).