To add the polynomials \( (5x^3 + x^2 - x) + (8x^2 + 3x + 1) \), we can combine like terms.
First, let's write out the two polynomials together:
\[ 5x^3 + x^2 - x + 8x^2 + 3x + 1 \]
Now, we will group the like terms:
- The \(x^3\) term: \(5x^3\)
- The \(x^2\) terms: \(x^2 + 8x^2 = 9x^2\)
- The \(x\) terms: \(-x + 3x = 2x\)
- The constant term: \(1\)
Now, we can combine everything together:
\[ 5x^3 + 9x^2 + 2x + 1 \]
The polynomial in standard form is:
\[ \boxed{5x^3 + 9x^2 + 2x + 1} \]