MathNet 2015-part-03 — 191 problems (EN–VI) Question 56

Let $f(x) = x^6 - x^5 - x^3 - x^2 - x$ and $g(x) = x^4 - x^3 - x^2 - 1$. If $a, b, c, d$ are the four roots of the equation $g(x) = 0$, find the value of $f(a) + f(b) + f(c) + f(d)$.