# B Basic Challenge of the Week #1 03/19/2017

1. Mar 3, 2017

### Greg Bernhardt

Prove that if $P(x), Q(x), R(x)$ and $S(x)$ are all polynomials such that $P(x^{5}) + xQ(x^{5}) + x^{2}R(x^{5}) = (x^{4} + x^{3} + x^{2} + x + 1)S(x)$, $x - 1$ is factor of $P(x)$.