I came across this polynomial
$X^4 + X^3 + 2X^2 + X + 1$
I tried to factor it using Rational root theorem, but it seems there are no roots possible. 1 or -1 don't work.
But I know for a fact that its composed of $(X^2 + X + 1) * (X^2 + 1)$ Wolfram Alpha factored it properly but can't seem to generate a step by step solution so I can understand what method was used?
I need 2 things:
1- A test that can tell me if this is factorizable. 2- A method to factor it.