三、初等因子的求法1、(引理1)若多项式 f(a),f,(a)都与 g (a),g,(a)互素，则(fi(a)gi(a), fz(a)g2(a)) =(fi(a), f(a)(gi(a), g2(a))证: 令 (fi(a)gi(a), fi(a)g2(a)=d(a),(fi(a), f(a)) = d;(a),(gi(a), g2(2))=d2(2),显然， d(a)d(a), 2(a)d(a).88.5初等因子区区§8.5 初等因子 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 ( ) ( ), ( ) ( ).    