To add the polynomials \( (5x^3 + x^2 - x) + (8x^2 + 3x + 1) \), we will combine like terms.
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Start with the first polynomial: \[ 5x^3 + x^2 - x \]
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Now add the second polynomial: \[
- (8x^2 + 3x + 1) \]
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Combine the like terms:
- For \( x^3 \): \( 5x^3 \)
- For \( x^2 \): \( x^2 + 8x^2 = 9x^2 \)
- For \( x \): \( -x + 3x = 2x \)
- For the constant term: \( 1 \)
Putting it all together, we have: \[ 5x^3 + 9x^2 + 2x + 1 \]
Thus, the final answer in standard form is: \[ \boxed{5x^3 + 9x^2 + 2x + 1} \]
This matches the second response option: 5x^3 + 9x^2 + 2x + 1.