A company's weekly profit $P$, in thousands of pounds, is modeled by the polynomial $P(n)=5n^3+k{n}^2+8n-30$, where $n$ is the number of units sold (in hundreds) and $k$ is a constant. A financial analysis reveals that when $P(n)$ is divided by $(n-2)$, the remainder is 2. Find the value of $k$.