# “Real” Cool Solution

This week I start complex numbers with my Precalculus class. This is a fun problem I found here (you can also go there for the solution when you’re ready).

Given $x^2+x+1=0$, find $x^3$.

## 3 thoughts on ““Real” Cool Solution”

1. This is a good problem, John. Another way to see the solution is to note that the polynomial x^2 + x + 1 is a factor of the polynomial x^3 – 1. Thus, all roots of the former are also roots of the latter. That is, any x that solves x^2 + x + 1 also solves x^3 = 1.