To correctly assess polynomial subtraction, we need to subtract the terms in the second polynomial from the terms in the first polynomial.
Let's perform the subtraction step-by-step:
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Start with the expression: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\).
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Distribute the negative sign across the second polynomial: \[ (2x^2 + 6x + 1) - 3x^2 - 3x - 9 \]
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Combine like terms:
- For the \(x^2\) terms: \(2x^2 - 3x^2 = -1x^2\)
- For the \(x\) terms: \(6x - 3x = 3x\)
- For the constant terms: \(1 - 9 = -8\)
Putting it all together: \[ -1x^2 + 3x - 8 \] or \[ -x^2 + 3x - 8 \]
Now, let's compare this result with the options given:
A. \(5x^2 + 9x + 10\) (Incorrect) B. \(x^2 + 3x + 8\) (Incorrect) C. \(-5x^2 + 3x - 8\) (Incorrect) D. \(-x^2 + 3x - 8\) (Correct)
Thus, the correct answer is D.
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