To determine which example correctly demonstrates polynomial addition, we need to add the polynomials \( (2x^2 + 6x + 1) \) and \( (3x^2 + 3x + 9) \) together.
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Add the coefficients of \(x^2\):
- \(2 + 3 = 5\)
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Add the coefficients of \(x\):
- \(6 + 3 = 9\)
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Add 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 we can compare this result to the provided options:
A. \( (2x²+6x+1) + (3x²+3x+9) = 5x²+9x+10 \) ✔️ Correct
B. \( (2x²+6x+1) + (3x²+3x+9) = 5x⁴+9x²+10 \) ❌ Incorrect
C. \( (2x²+6x+1) + (3x²+3x+9) = 13x²+9x+10 \) ❌ Incorrect
D. \( (2x²+6x+1) + (3x²+3x+9) = -x²+3x-8 \) ❌ Incorrect
Thus, the correct answer is A.
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