<s>[INST] Finding the roots $x^4-4x^3-x^2-8x+4=0$ (contest math) So the problem is :
$x^4-4x^3-x^2-8x+4=0$, find all solutions
A tip that I have gotten, is to divide both sides by $x^2$. I've tried so, but I do not manage to see any further. Do anyone know how this tip could help me?
(Yes, I'm aware that the polynomial above can be factorized into two degree 2 polynomials, which promptly gives me the answer. But that factorization would be extremely hard to spot, which is why I'm asking about the dividing)
Thanks in advance :)
Edit: meant to write $x^2$, not $2$
 [/INST] Divide $x^4-4x^3-x^2-8x+4=0$ with $x^2$ in order to get the following $x^2-4x-1-\frac{8}{x}+\frac{4}{x^2}=(x+\frac{2}{x})^2-4(x+\frac{2}{x})-5=(x+\frac{2}{x}-5)(x+\frac{2}{x}+1)$. Finally, result is $(x^2-5x+2)(x^2+x+2)$.
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