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To find the sum of the two polynomials \((4n^3 - 2n^2 - 5n) + (2n^4 + 6n^2 + 2n + 8)\), we first align the like terms:
1. **First Polynomial**:
\(4n^3 - 2n^2 - 5n\)
2. **Second Polynomial**:
\(2n^4 + 6n^2 + 2n + 8\)
Now, we can rewrite the expression by combining them:
\[
(4n^3 + 2n^4 - 2n^2 + 6n^2 - 5n + 2n + 8)
\]
Next, we combine the coefficients of like terms:
- **For \(n^4\)**:
\(2n^4\)
- **For \(n^3\)**:
\(4n^3\)
- **For \(n^2\)**:
\(-2n^2 + 6n^2 = 4n^2\)
- **For \(n\)**:
\(-5n + 2n = -3n\)
- **Constant term**:
\(8\)
Now we can write the sum:
\[
2n^4 + 4n^3 + 4n^2 - 3n + 8
\]
Therefore, the sum of the polynomials is:
\(\boxed{2n^4 + 4n^3 + 4n^2 - 3n + 8}\)