need help solving this function....

A polynomial f(x) satisfies the equation f(x)+(x+1)3=2f(x+1). Find f(10).

Write as (you may also add or higher degrees), write the equation in terms of , ..., and equate the coefficients of the corresponding monomials. You'll get a system of four linear equations in , ..., .

ok, emakarov has the idea...
try, but if you want to learn the full technique here it is (Hi)

Spoiler:

your question: find if

now, you have stated that is a polynomial, I am assuming it is a quadratic polynomial (this dosen't always work though...but school problems are generally that way(Wink) )
so let
so
now according to your equation,

(you will get this by expanding and simplifying the above equation)
now you can see that the right hand side has no in it, so a must be equal to 0 in order to equate it.
if , the equation shortens to
we know the equation to be true for all values of
so put , it becomes
put , it becomes or and so or
so we get and our function becomes .if ,