例如，若f(x),g(x)的标准分解式分别为f(x)=ap"(x)p(x)..p,(x), r, ≥0g(x)= bpt(x)p2*(x)..-p,*(x), 1, ≥0则有(f(x),g(x))= p(x)p,(x)..p, (x),, = min(r,l.),i= 1,2,..,s[f(x),g(x)] = pl" (x)p,"2 (x)... p," (x),u, = max(r,l,),i = 1,2,..,sf(x)|g(x)αr, ≤l, i=1,2,..",sRF81.5因式分解定理§1.5 因式分解定理 ( ) ( ) , 1,2, , i i f x g x r l i s   = 例如，若 f x g x ( ), ( ) 的标准分解式分别为 1 2 1 2 ( ) ( ) ( ) ( ), 0 s r r r s i f x ap x p x p x r =  1 2 1 2 ( ) ( ) ( ) ( ), 0 s l l l s i g x bp x p x p x l =  则有 ( ) 1 2 1 2 ( ), ( ) ( ) ( ) ( ), s s f x g x p x p x p x    = i i i = = min , , 1,2, , (r l i s )   1 2 1 2 ( ), ( ) ( ) ( ) ( ), u u us s f x g x p x p x p x = u r l i s i i i = = max , , 1,2, , ( )