Value of an expression involving polynomial function If $f(1) = 10$, $f(2) = 20$, $f(3) = 30$ and $f(x) =(x^4 +ax^3 + bx^2 +cx + d) $ then find the value of $\frac{f(12) + f(-8)}{(10)}$
My attempt: I tried to substitute the values in the numerator but could not get rid of d. Since there are three known values I don't know how to get values of all four constants. Any help will be appreciated. 
 A: Hint
Use the three conditions and solve for $a,b,c$ as functions of $d$.
Using these results, compute the expression and you will get the value already given by 
Satish Ramanathan. By magic, $d$ disappears !
Edit
For the fun of it, compute $f(A)+f(B)$; the result is a function of $d$. Now, say that you want the result to be independent of $d$; so, take the derivative of the obtained expression and set it equal to $0$. You would find that one condition corresponds to $A+B=4$.
A: First you need to understand that, fundamentally, there exists an infinity of polynomes of degree $n$ that goes through $n$ distincts points (I strongly advise you to have a look at interpolation polynomes). 
In your particular case, you have $4$ unknowns and $3$ equations. There is no unique solution. 
Since this is the case, it means that either your problem is incomplete, or you can choose arbitrarely one of the polynomes that satifies the conditions. 
And there is one particular very very easy polynome you can find. 
