2020 AMC 12B 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} \qquad \textbf{(B) } \text{a multiple of 10} \qquad \textbf{(C) } \text{a prime number} \qquad \textbf{(D) } \text{a perfect square} \qquad \textbf{(E) } \text{a perfect cube}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.