西安毛子科技大学XIDIANUNIVERSITY三、初等因子的求法1、(引理1)若多项式 fi(a),f()都与 gi(2),g2(a)互素，则(fi(a)gi(a), f2(a)g2(a)) =(fi(a), 2(a))(gi(a), g2(a)证: 令 (fi(a)gi(a), f(a)g2(a))=d(a),(fi(a), fe(a)) = d(a),(gi(a), g2(2)= d,(2),显然，（d,(a)]d(a), d,(a)d(a)1、(引理1)若多项式 f f 1 2 ( ), ( )   都与 1 2 g g ( ), ( )   互素，则 三、初等因子的求法 ( f g f g f f g g 1 1 2 2 1 2 1 2 ( ) ( ), ( ) ( ) ( ), ( ) ( ), ( )         ) = ( )( ) 证：令 ( f g f g d 1 1 2 2 ( ) ( ), ( ) ( ) ( ),      ) = ( f f d 1 2 1 ( ), ( ) ( ),    ) = ( g g d 1 2 2 ( ), ( ) ( ),    ) = 显然， 1 2 d d d d ( ) ( ), ( ) ( ).    