Need help at factorial

Question

$$\frac{ (2+x)!}{x!}$$ is there any formula for calculating this?

I think : x!(x+2)/x! then results in x+2...is this true?

Answer 1

Assuming $x$ is a positive integer, then

$$ \frac{ (2+x)!}{x!} = \frac{(2+x)(1+x)x!}{x!} = (2+x)(1+x) = 2 + 3x + x^2$$

Notice by definition $n! = n \times (n-1) \times (n-2) \times ... \times 1 $