Need help solving a bi-quadratic polynomial.... The polynomial to be factorised as a product of two factors is- $$x^4+3x^2+6x+10$$. I checked the solution in wolfram alpha to be- $$(x^2-2x+5)(x^2+2x+2)$$. I tried to factorise it by expressing it as a sum of two squares $$(x^2+1)^2+(x+3)^2$$. But I cannot solve it. Please help. Thanks a lot in advance.   

The given polynomial $x^4+3x^2+6x+10$
Can be written as
$ x^4+2x^3+2x^2-2x^3-4x^2-4x+5x^2+10x+10$
$= x^2(x^2+2x+2) - 2x(x^2+2x+2) +5(x^2+2x+2)$
$=(x^2+2x+2)(x^2-2x+5) $
