解  原式[tex=9.571x1.357]xe59p/pO3QP0JOmSFHwoSgvvb9MgrYjV/8lqLuLv3c4=[/tex]是实数域上[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]次多项式. 求出它的全部复数根，即可得到复数域上的分解式. 再将相互共轭的虚系数因式相乘, 就得到实数域上所有的不可约因式.由 [tex=5.357x1.357]zpcaEalQ9zk785caACdZxesrZikn8x1PVyNg/KQ4Tt0=[/tex] 知[tex=1.286x1.143]JD4gmVNWunFIZYp5E0BI3Q==[/tex] 不是方程 [tex=3.143x1.357]GaUU+prLnDPZRkTgFIz5aw==[/tex]的根，因此可以方程两边同除以 [tex=3.429x1.357]dhG7GqBFvL8rS1lgthd3EA==[/tex]化为[tex=26.214x2.786]TlQng4sRYS8B+KnJFZ8+Z9sfVVKAEIsOEOLKLLO//GKHZb5IwJkpO91P5HwwxnIIzPiT0EYdxIPR6/ZUw40ICS4T+blrFI2yse5lcpj2p4V6tbdX146wrrL43yaDI470rHG8o1gZkjMjuAIez6kPKdBGkJr4dkTZYzYyWONJqttK9Q/QNQCsSnssZVZL5dlmVq2Zz6Z8KvKdl74fHIWM5Q==[/tex] 其中 [tex=27.571x2.429]YW9h0w20WGJaY8kEcpVHtyUL23sLRpDShD6+4PzzYV6+Q80rVwvdaZKiGngpR+aOisrwjx6e7+EmQYN9GyuK45Qe5K3chQtETFnUonYNWyUa/GL5CV5sMicvOBVZE/YoPyXA6mAJVpJMpHZpZ+oVhHkX82eDH/jgFQQgnB67tQWvPEkugRVGIgehpXSXl6B7[/tex]对每个[tex=4.571x1.214]/X+kzGHeoFvFUAhRc3wSfh5QAba5b8AtdJVQ4/Dq/SE=[/tex]由 [tex=4.071x2.429]PvFOI6R7lzx6jSmTgKLuZpjkDJsdjRazKrjZxetw+Dw=[/tex]解出[tex=18.0x6.143]lPyVZlf8OZi9kBlPpytDSh51xAYzOKWdrp36F2omKpNcjfcTB7l5+O8rRjiyFxjEHaKJVTwvsanxUFOMwaHfeNhPM5i7ryNMjz/Esvno+OU9zoL4ubnJ1FfsRMQpHsqgtKujffWrtCKu4lOiSH3OGJUdm4TGjyjVdztt5iSQq1HQx7RbW9CmJnjjlqjsoLgknHchIBY547j1hj2tv3X8guHNBvj3r5NtGYjKysaiP4EsoufPA5NcZICTLg1a+LG/onOXeTh4Y22wUMo24W/G/M/xS1ZSgw1DBdlaqA1XaBs1Iy2/Txqhk87B0NODSHr9UKGlmhZm5bcTzVPTkoYnSnnFhTdJObLJdS22/0Y4dIwWmq/5LMqlRfr2ZksSyufEB1fTXFM0pmllCIlHaJwcuhKlRnd6Xv68H7i2QSRrUad+urQAslw/1bl6KGFaNY7xWXV8MB0Ppmlkna6dhaO/3SCZkFMhHUwp/6eVxBdfHcU=[/tex][tex=11.143x2.429]x7PBwcLM5kjrBNd0hX/TthnE4Ks7BfIfoL5eME9kD4yH6yLvD3QHhUdcIeL5iKLnYE0DcdJAAefvuCOa+Dg4Mw==[/tex] 是 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 的 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 个不同的复数根.[tex=6.429x1.357]HvJe+PlMLXMDs4MSW1zyReUwEecUMmXqdYm40zAOYXA=[/tex]的首项系数为 2,在复数范围内分解为[tex=25.786x2.786]EDuemOSqBJdlYxNR2f99u/BOzKBvVOam9dkmIVZXqw89s4lWQ07a92aNfjNTTns7JLXXQdVHayJq71BObxXY/CYlUXwRa7sbgWoLxCuST5TRchHME/8v2gqM7meZdt/XOetON5Zc4m8aOFALSfBf5fjo//FeQGb95a/5o5TOuOcCQ1xm3g1qe+qfEqmJ5gY/[/tex]每个[tex=5.929x2.429]+QSDL/oqbKxgLQJu8Af9L9ZLHLrXkG6XxXV7zFueNQAO3JmhxBzqwiGzUIiISozt[/tex]与 [tex=25.286x2.786]+QSDL/oqbKxgLQJu8Af9LxOrgSEx0LVU9vK7NsUHrQqhAACYJMUc5+Ij0STJ4Zx5wQItA3Qf9k7KKw1mQFVjrlbZVJfIM4QJZDTZSIRjerPeGkZyFQ47PNktZmupxqFr0pUq1oLENTKO3gFF2ziROtCGhD7eqcWDqUnCtDL0xZw=[/tex]互为相反数，相互共轭. 当 [tex=4.571x2.143]ij2uSjh1F/JPot8U70PmVWRfv37npl6bl5nvkBc20zo=[/tex]时, [tex=8.5x2.429]kHDhINbQPzRVgfSVHjBQhzfZ3071cgiYz6cegz0IqI9FxYVPNRJKQrJ6q2IN6ejC[/tex] 相互共轩的虚根 [tex=6.714x2.429]UQHBeZSkfEuzuKCyXqCtYPjZOkzL9lLLfKh7vpNuYwdMWdXaDyqMoH3NOcmFr8AL[/tex] 对应的一次因式的乘积[tex=31.071x2.786]y9FPTRfVfaPQ1Fo++5PWTKXxedt4Q6oj0g+DCC8AcuPxJ5v6FqfsF1KAQFEDPLPtxJ7Eb1J4BKa0qcSXLHHjYZknvWO3sSN+l2KCIB2HjpKo/7hn+3GpNB16Rjj5ojQ5lEFu0VhFCHoAJOIAsQVXCARvEEyHlZiLfNiNXY+04nX100vktO/vbfoFGFthn0tPNL77g5UGWOWvR4p/hhKb9Q==[/tex]是实数域上不可约二次多项式. 当[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]为偶数时，[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 在实数域上分解为[tex=0.857x2.143]SHy24wQWjYBVVxFBAkTfJA==[/tex] 个不可约二次因式 [tex=8.143x2.214]npp5KuJ4PtzjTP5MaeS6Zd5PxWMnhDyhB/huozw4pWoJfNDIN0wqKBoCA9TjxZO/iIp/+WoJv8jpfoChcmis5w==[/tex]的乘积[tex=26.714x2.786]EDuemOSqBJdlYxNR2f99uy47T5eUIJPfN9fwuICBAb9O3+orhF5zX+2c72l/kqvkc5iKR7z3fae443vTCAghNbSP7wHrGdE54wRC1uiWkY80KYQV0LKUre3KHmoU8BHOXKAQGIrwoZIwhH16b8411sXDBYm6sp4UM5D3mhzneH6E1kHRoh0uxZwCe37z/hvgVGS5GeBF3kNt0MOYPQVCcw==[/tex]当 [tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex] 为奇数时, [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]的常数项为 0, 有实根 [tex=1.071x1.357]q44MuEJjNceuaani2si7VwjuMnmgsrT72JFLI+pobDw=[/tex] 当 [tex=3.643x2.357]mqFBTaPTkNWFZ+bJII+u/eljEwHvR6/e77AD6lVL7nU=[/tex]时的[tex=13.5x2.786]cq8l+zFtbRFR+iKpE9d7JCuqASbwOyKGXudEgePAbtf02UAi0R3nYwJOn67CDjfoldql5wh7a8s3OTakKRri4+9H82KeleA//X1NX+s9fWg=[/tex]在实数域上被分解为一次因式与[tex=2.143x2.357]SPrL5FNmvzku73NiUojDaw==[/tex] 个不可约二次因式 [tex=9.714x2.786]npp5KuJ4PtzjTP5MaeS6Zd5PxWMnhDyhB/huozw4pWqHHiJsooXeTbOqXpWm/EB6h4k8nuSK/Fa/9EIL413qrg==[/tex]的乘积:[tex=27.286x2.786]Csb3Bfj0CkyfmG4bn98yJ1BX+ugjYVFDC6PE07vTfhPIR051NUmvHuv1ZLvQElFaQk6biwfb9uE6cCgVClsXtThprgEpY2G9BsycOQWjrGyCM9MxRXVPa8DfmMLeNT7L6zU+4zG9NzV1sQrgqkATqDIkUH/hrHsHfKvIUOrYEZs7tceEWxt4EzptqbVcCJRa6PyNxHo1t5QlKKLuO5uqD0v3oGaLbFsNPUOiC5vV3Ks=[/tex]