MQ2 --- Factorization

x⁴ + 2x² + 3 + 2x⁻² + x⁻⁴= (x⁴ + 2x² + 1) + (2 + 2x⁻²) + x⁻⁴= (x² + 1)² + 2 x⁻² (x² + 1) + x⁻⁴= (x² + 1 + x⁻²)²

2012-04-30 11:54:29 補充：
= (x² + 2xx⁻¹ + x⁻² - 1)²

= ( (x + x⁻¹)² - 1 )²

= ( (x + x⁻¹ - 1 )(x + x⁻¹ + 1 ) )²

2012-04-30 11:55:42 補充：
x⁴ + 2x² + 3 + 2x⁻² + x⁻⁴
= (x⁴ + 2x² + 1) + (2 + 2x⁻²) + x⁻⁴
= (x² + 1)² + 2 x⁻² (x² + 1) + x⁻⁴
= (x² + 1 + x⁻²)²
= (x² + 2xx⁻¹ + x⁻² - 1)²
= ( (x + x⁻¹)² - 1 )²
= ( (x + x⁻¹ - 1 )(x + x⁻¹ + 1 ) )²

中招了