1. **Problem:** Find the expression for $f(n) = 4n^3 - 2n^2 + n - 5$ and simplify or analyze it if needed. 2. **Formula and rules:** This is a polynomial function of degree 3. Polynomials are expressions consisting of variables and coefficients combined using addition, subtraction, and multiplication by powers of the variable. 3. **Intermediate work:** The function is already simplified as $f(n) = 4n^3 - 2n^2 + n - 5$. 4. **Explanation:** This function takes an input $n$ and outputs a value calculated by multiplying $n$ cubed by 4, subtracting twice $n$ squared, adding $n$, and then subtracting 5. 5. **Final answer:** The function is $f(n) = 4n^3 - 2n^2 + n - 5$.