To determine which example correctly demonstrates polynomial addition, we should add the two given polynomials in each option.
Let's add the polynomials:
\[ (2x^2 + 6x + 1) + (3x^2 + 3x + 9) \]
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Combine the \(x^2\) terms: \[ 2x^2 + 3x^2 = 5x^2 \]
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Combine the \(x\) terms: \[ 6x + 3x = 9x \]
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Combine the constant terms: \[ 1 + 9 = 10 \]
So the correct addition results in: \[ 5x^2 + 9x + 10 \]
Now, let's examine the options:
A. \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10\) (Correct)
B. \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^4 + 9x^2 + 10\) (Incorrect, exponent of \(x\) is wrong)
C. \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = -x^2 + 3x - 8\) (Incorrect, all terms are wrong)
D. \((2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 13x^2 + 9x + 10\) (Incorrect, \(x^2\) terms are added incorrectly)
Only option A is correct.
So the answer is: A. (2x^2 + 6x + 1) + (3x^2 + 3x + 9) = 5x^2 + 9x + 10