How to factorize x^4 + 3x^2 + 4

Since 3x^2 can be written as 4x^2 - x^2, we can write

x^4 + 3x^2 + 4 = x^4 + 4x^2 + 4 - x^2

= (x^2 + 2) ^ 2 - (x)^2 , using (A + B)^2 = A^2 + 2AB + B^2 where A = x^2 and B = 2

= (x^2 + 2 + x) (x^2 + 2 - x) , using A^2 - B^2 = (A + B)(A - B)

= (x^2 + x + 2) (x^2 - x + 2)  Ans., using commutativity