<s>[INST] $f(x) =ax^6 +bx^5+cx^4+dx^3+ex^2+gx+h $, find $f(7)$. Problem : 

Given a polynomial $f(x) =ax^6 +bx^5+cx^4+dx^3+ex^2+gx+h$
  such that $f(1)= 1, f(2) =2 , f(3) = 3, f(4) =4, f(5)=5, f(6) =6$.
Find $f(7)$ in terms of $h$.

My approach: 
We can put the values of $f(1) = 1$ in the given equation and $f(2) = 2$, etc. But this is quite time consuming by making six different equations and then solve them to get the values of $a,b,c,d,e,g,h$.  Please suggest some alternate solution for this.
 [/INST] Hint:
$$f(x)=K(x-1)(x-2)(x-3)(x-4)(x-5)(x-6)+x$$
For some constant K. Plug in $x=0$ to get K and then plug $x=7$ to get answer. 
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