<s>[INST] If $ x^4+x^3+x^2+x+1=0$ then what is the value of $x^5$ If $$x^4+x^3+x^2+x+1=0$$ then what's the value of $x^5$ ?? 
I thought it would be $-1$ but it does not satisfy the equation
 [/INST] $x^4+x^3+x^2+x+1 = 0$
Multiply everything by $x$
$x^5+x^4+x^3+x^2+x = 0$
Add $1$ to both sides:
$x^5+x^4+x^3+x^2+x+1 = 1$
$x^5+(x^4+x^3+x^2+x+1) = 1$
$x^5+(0) = 1$
$x^5=1$
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