<s>[INST] Help factorising a sixth degree polynomial I have to factorise- $$x^6+5x^3+8$$Answer is $$(x^2−x+2)(x^4+x^3−x^2+2x+4)$$.I have also used factor theorem.Please help me.Thanks in advance.
 [/INST] Break the equation $x^6+5x^3+8$ into $x^6+8-x^3+6x^3$. It then comes into the form $a^3+b^3+c^3-3abc$. Factorise it using the formula $a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$. 
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