5)若 f(x)Ig,(x), i=1,2,..",r则对 Vu,(x)eP[x], i=1,2,,r 有f(x)/(u (x)gi(x)+u,(x)g2(x)+...u,(x)g,(x)注：反之不然．如 f(x)=3x-2,g(x)= x2 +1, g2(x) =2x+3,u(x)=-2, u(x)=x,(u, (x)gi(x)+ u,(x)g,(x) = -2 +3x,: f(x)I(u(x)gi(x)+uz(x)g2(x)但 f(x)+gi(x), f(x) +g2(x).下81.3整除的概念§1.3 整除的概念 5) 若 ( ) | ( ) 1,2, , i f x g x i = r ， 则对 ( ) [ ], 1,2, ,   u x P x i = r i 有 ( ) 1 1 2 2 ( ) | ( ( ) ( ) ( ) ( ) ( )) r r f x u x g x u x g x u x g x + + 注：反之不然．如 2 1 2 g x x g x x ( ) 1, ( ) 2 3, = + = + ( ) 1 1 2 2 ( ( ) ( ) ( ) 2 3 , u x g x u x g x x + = − +  + f x u x g x u x g x ( ) | ( ) ( ) ( ) ( ) ( 1 1 2 2 ) f x x ( ) 3 2, = − ( ) 1 2 u x u x x = − = 2, ( ) , 1 2 但 f x g x f x g x ( ) | ( ), ( ) | ( )