# Factoring the quintic polynomial $x^5+4x^3+x^2+4=0$

I am trying to factor

$$x^5+4x^3+x^2+4=0$$

I've used Ruffini's rule to get

$$(x+1)(x^4-x^3+5x^2-4x+4)=0$$

But I don't know what to do next.

The solution is $(x+1) (x^2+4) (x^2-x+1) = 0$. I've tried using the completing square method but with no result. Could you give me hints?

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Since you know the solution just try to go backwards to the previous step –  math137 Feb 18 at 17:23

Hence proved

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