1. **State the problem:** We are given the cubic expression $x^3 + 22x + n$ and need to analyze or solve it depending on the context (e.g., find roots, factor, or determine $n$ for specific properties). 2. **Formula and rules:** For cubic polynomials of the form $x^3 + ax^2 + bx + c$, the roots can be found using the cubic formula or factoring if possible. Here, the polynomial is $x^3 + 0x^2 + 22x + n$. 3. **Intermediate work:** Since there is no $x^2$ term, the polynomial is depressed cubic. To find roots or factor, one might try rational root theorem or substitution. 4. **Explanation:** Without a specific question (e.g., find roots, factor, or determine $n$ for a root), we cannot proceed further. If you want to find roots for a specific $n$, please provide $n$ or the condition. Since the problem is incomplete, this is the analysis for the given expression.