MQ17 --- Factorization (MW)

2012-05-26 8:00 pm
Difficulty: 30%Factorize x³ + x² + x- x⁻¹ - x⁻² - x⁻³.

回答 (1)

2012-05-26 9:19 pm
✔ 最佳答案
x³ + x² + x - x⁻¹ - x⁻² - x⁻³
= x(x² + x + 1) - x⁻³(x² + x + 1)
= (x - x⁻³) (x² + x + 1)
= x⁻³ (x⁴- 1) (x² + x + 1)
= x⁻³ (x² - 1) (x² + 1) (x² + x + 1)
= x⁻³ (x - 1) (x + 1) (x² + 1) (x² + x + 1)


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