<s>[INST] How do I factorise $r^4+r^2+1$? How do I factorise $r^4+r^2+1$ ?
$(r^2+r+1)(r^2-r+1)$ gives $r^4+r^2+1$
But how to split it into these factors?
I generally find roots and then write the factors, but $r^4+r^2+1$ seems to have no real root.
Thanks!
 [/INST] $$x^4+x^2+1=\frac{x^6-1}{x^2-1}=\frac{(x^3-1)(x^3+1)}{(x-1)(x+1)}
=(x^2+x+1)(x^2-x+1).$$
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