<s>[INST] Finding the roots of $x^5+x^2-9x+3$ I have to find all the roots of the polynomial $x^5+x^2-9x+3$ over the complex. To start, I used Wolfram to look for a factorization and it is $$x^5+x^2-9x+3=(x^2 + 3) (x^3 - 3 x + 1)$$
I can take it from here employing the quadratic and cubic formula, but how can I get the same answer w/o using any software?
 [/INST] It can be factorize by adding and subtracting $3x^3$
$$x^5+x^2-9x+3=x^5-3x^3+x^2+3x^3-9x+3=x^2(x^3-3x+1)+3(x^3-3x+1)=(x^2 + 3) (x^3 - 3 x + 1)$$
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