Find a sufficient statistic. Suppose that $X_1,\ldots,X_n$ is a random sample from a distribution with pdf 
$$ f(x;\theta)=\frac{\theta^3}{2}x^2e^{-\theta x}, \quad 0<x<\infty$$ 
where $0<\theta<\infty$
Find a sufficient statistic for $\theta$.
I would appreciate an simple explanation of sufficiency using this example. 

A Fisher factorization is as follows:
$$
\underbrace{\left(\frac{\theta^3} 2 \right)^n e^{-\theta\sum_{i=1}^n x_i}}_\text{(A)} \,\,\,\underbrace{\left(\prod_{i=1}^n x_i^2\right)}_\text{(B)}
$$
Factor $\text{(A)}$ depends on $x_1,\ldots,x_n$ only through their sum. Factor $\text{B}$ does not depend on $\theta.$
