Factorize : $x^6 − 10x^3 + 27$ I want to factorize $$x^6 − 10x^3 + 27$$ 
I tried two methods , first I let $y=x^3 $ and converted it into a quadratic but the solutions are not real . 
The second method I tried was getting it to the form $a^3+b^3+c^3-3abc$ but I could only get close ( $(x^2)^3+(x)^3+3^3-3(x^2)(x)(3)$ but that is actually $x^6-8 x^3+27$ , close but not exact )  
I'm run out of ideas , so any help is appreciated .
Note : I know that the answer is $$(x^2+2 x+3) (x^4-2 x^3+x^2-6 x+9)$$ , but I want to know how !

In such cases, we can start with 
$$(x^2)^3+(ax)^3+b^3-3\cdot x^2\cdot ax\cdot b=x^6+x^3(a^3-3ab)+b^3$$
Comparing with the given expression, $b^3=27, a^3-3ab=-10$
We know, the only real value of $b$ is $3\implies a^3-9a+10=0$
Clearly, $a=2$ satisfies the last equation 
