USAMO 1976 Problem 5

The polynomials $a(x), b(x), c(x), d(x)$ satisfy $a\left(x^{5}\right)+x b\left(x^{5}\right)+x^{2} c\left(x^{5}\right)=\left(1+x+x^{2}+x^{3}+x^{4}\right) d(x)$. Show that $\mathrm{a}(\mathrm{x})$ has the factor $(\mathrm{x}-1)$.