How to factorize x^4 + 5x^2 + 9 ?

x⁴ + 5x² + 9

= x⁴ + 5x² + 9 + x² - x², adding and subtracting x²

= x⁴ + 5x² + x² + 9 - x², using commutativity

= (x⁴ + 6x² +9) - x² , adding 5x² and x²

= [ (x²)² + 2.x².3 + 3² ] - x²,  using (A^m)ⁿ = A^mn and factorizing 6

= (x² + 3) ² - x², using (A + B)² = A² + 2AB + B²

= (x² + 3 - x)(x² + 3 + x), using (A - B)² = (A - B)(A + B)

= (x² - x + 3)(x² + x +3), Ans. , using commutativity