how to obtain this form $c_0+c_1x+c_2x(x-1)+c_3x(x-1)(x-2)+c_4x(x-1)(x-2)(x-3)$ $$\begin{align*}f(x)=x^4-2x^3+x-1\end{align*}$$
express $f(x)$ as the following form
$$\begin{align*}c_0+c_1x+c_2x(x-1)+c_3x(x-1)(x-2)+c_4x(x-1)(x-2)(x-3)\end{align*}$$
I know how to express as power series by Ruffini's rule.

Hint: Let $x=0$. Note that $f(0)=-1$. See what that tells you about $c_0$. 
Let $x=1$, and use the information to find $c_1$.  
Continue, finding $c_2$ and $c_3$. Finding $c_4$ uses a somewhat different idea. 
