AMC 12 2020b Problem 6

For all integers $n \geq 9,$ the value of $$\frac{(n+2)!-(n+1)!}{n!}$$is always which of the following?

$\textbf{(A) } \text{a multiple of 4} \textbf{(B) } \text{a multiple of 10} \textbf{(C) } \text{a prime number} \textbf{(D) } \text{a perfect square} \textbf{(E) } \text{a perfect cube}$