Question

Cum descompui în produs de factori ireductibili expresia x^8 - 2x^6 + 2x^2 -1​

Answer 1

x⁸ - 2x⁶ + 2x² - 1 =

= x⁸ - 1 - 2x²(x⁴ - 1)

= (x⁴ - 1)(x⁴ + 1) - 2x²(x⁴ - 1)

= (x² - 1)(x² + 1)(x⁴ + 1) - 2x²(x² - 1)(x² + 1)

= (x - 1)(x + 1)(x² + 1)(x⁴ + 1) - 2x²(x - 1)(x + 1)(x² + 1)

= (x - 1)(x + 1)(x² + 1)[(x⁴ + 1) - 2x²]

= (x - 1)(x + 1)(x² + 1)(x⁴ - 2x² + 1)

= (x - 1)(x + 1)(x² + 1)(x² - 1)²