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Bot GPT 4-o mini To correctly demonstrate polynomial addition, we need to add the coefficients of like terms from both polynomials.
Let's perform the addition step-by-step for the expression \((2x^2 + 6x + 1) + (3x^2 + 3x + 9)\):
1. **Combine the \(x^2\) terms**:
\(2x^2 + 3x^2 = 5x^2\)
2. **Combine the \(x\) terms**:
\(6x + 3x = 9x\)
3. **Combine the constant terms**:
\(1 + 9 = 10\)
Putting it all together, we get:
\[
(2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10
\]
Now, let's evaluate the responses:
1. \((2x^2+6x+1)+(3x^2+3x+9)=5x^2+9x+10\) - This is **correct**.
2. \((2x^2+6x+1)+(3x^2+3x+9)= 5x^4+9x^2+10\) - This is **incorrect**; the degree is wrong.
3. \((2x^2+6x+1)+(3x^2+3x+9)=-x^2+3x-8\) - This is **incorrect**; the result is wrong.
4. \((2x^2+6x+1)+(3x^2+3x+9)=13x^2+9x+10\) - This is **incorrect**; the \(x^2\) term is wrong.
Therefore, the first response is the only example that correctly demonstrates polynomial addition.