Factoring polynomial

Question

X^{6  -} 9x⁴  - x²  +. 9 = 0

Answer 1

x⁶ - 9x⁴ - x² + 9 = 0

= x⁴(x²-9) - (x²-9)  factor out x⁴ in the first two terms and a (-1) in the last two terms.                    

= (x⁴-1)(x²-9)       collect like terms. Ex. a(x²-c) - b(x²-c) = (a-b)(x²-c)

=(x²+1)(x²-1)(x+3)(x-3)       Difference of Two Squares: (a²-b²) = (a-b)(a+b).     x⁴ = (x²)², so x²= a                     (x²-9) = (x-3)(x+3)    (x⁴-1) = (x²+1)(x²-1)

=(x²+1)(x+1)(x-1)(x+3)(x-3)        Difference of Two squares again for (x²-1) = (x+1)(x-1)

 

 

Answer 2

x^6 - 9x^4 - x^2 + 9

= x^4(x^2 - 9) - (x^2 - 9)

= (x^4 -1)(x^2 - 9)

= (x^2+1)(x+1)(x-1)(x+3)(x-3)