Let $P(x) = x^3 - 2x + 1$ and let $Q(x) = x^3 - 4x^2 + 4x - 1$. Show that if $P(r) = 0$ then $Q(r^2) = 0$.
Source: 2020 New Zealand MO Round 2 p1 NZMO
Tags: algebra, polynomial
Let $P(x) = x^3 - 2x + 1$ and let $Q(x) = x^3 - 4x^2 + 4x - 1$. Show that if $P(r) = 0$ then $Q(r^2) = 0$.