Polynomial and Function I have been give a question if 
  $ f(x) = x^3-1 $
then show 
$$  \frac {f(b) - f(a)} {b-a} =b^2+ab+a^2 $$ 
how to show that the above fraction is equal to that polynomial if $ f(X) = x^3-1 $ ?

It results from the high-school identity:
$$x^3-y^3=(x-y)(x^2+xy+y^2).$$
More generally:
$$x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y+x^{n-3}y^2+\dots+xy^{n-2}+y^{n-1}).$$
