多项式习题课2.pdf

SNJ K Home Page I K JJII JI 11 30 w 4 SSSKKK Zuo Liancui College of Mathematical Science Tianjin Normal University Mar 25 2011 SNJ K Home Page I K JJII JI 12 30 w 4 Main Contents 1 SNJ 2 K SNJ K Home Page I K JJII JI 13 30 w 4 1SNJ 1 F g 0 p x e UL F g Kp x F f x ef x g1 x g2 x 0 deggi x 0 f x F 5 ek f x p1 x p2 x ps x q1 x q2 x qs x K7ks t gS k pi x ciqi x i 1 2 s 0 6 ci F IO f x apk1 1 x pks s x 3 F p x f x k epk x f x pk 1 x f x k K k 1 p x f x k 1 p x f x k 0 p x f x SNJ K Home Page I K JJII JI 15 30 w 4 n6 e p x f x k k 1 Kp x f 0 x k 1 1 p x f x p x f x f 0 x ep x f x f 0 x k Kp x f x k 1 2 p x f x k p x f x f 0 x f k 1 x f k x 3 f x f x f 0 x p l g x f x f x f0 x Kf x g x k g x SNJ K Home Page I K JJII JI 16 30 w 4 eg x ap1 x ps x f x f 0 x pl1 1 x plt t x Kt s f x apl1 1 1 x plt 1 t x pt 1 x ps x 4 n7 n x c f x uf c n ef c 0 Kc f x n c f x x c f x ex c f x k K c f x k c f x k c f x f 0 x f k 1 x c f k x SNJ K Home Page I K JJII JI 17 30 w 4 n8 F ng f x 3F kn n9 ef x g x g Ln 3 p n 1 c1 cn 1 Kf x g x 5 n n 0 g 3E k n 0 g 3E k g E k g E ng 3E C Tkn E IO f x a0 x c1 k1 x cs ks SNJ K Home Page I K JJII JI 18 30 w 4 6 R J n e X f x kJ K f x k R f x a x 1 k1 x 2 k2 x s ks x2 p1x q1 l1 x2 prx qr lr i pj qj R ki lj Z p2 j 4qj 0 X 1 f x g x F x 7k f x g x 1 3 m f x gm x y f x pm x p x F X 1 K u g x F x o p x g x 1 op x g x f x g x 1 f x gm x f x f x pk1 1 x pks s x eys 1 K es 1 K ug x p1 x k SNJ K Home Page I K JJII JI 117 30 w 4 f x g x 6 1 u m k f x gm x g s 1 f x pk1 1 x 7 f x F ng K f 0 x f x f x a x b n y f x a x b n f 0 x na x b n 1 f 0 x f x f 0 x f x a f x X Kf0 x X na f x 1 nf 0 x x b SNJ K Home Page I K JJII JI 118 30 w 4 l f x f 0 x 1 naf 0 x g x f x 1 naf 0 x a x b f x k x b degf x n f x a x b n 8 y g2 x f 2 x g x f x y g x f x 3h x f x g x h x of 2 x g2 x h2 x l g2 x f2 x f x apk1 1 x pks s x K SNJ K Home Page I K JJII JI 119 30 w 4 f 2 x a2p2k1 1 x p2ks s x g2 x f 2 x g x p1 x ps x g x bpr1 1 x prs s x ri 0 K g2 x b2p2r1 1 x p2rs s x dug2 x f 2 x o2ri 2ki ri ki i 1 2 s g x f x n y u m kgm x f m x g x f x 9 y g 0 X 1 f x u g x h x F x df x g x h x f x g x m f x hm x SNJ K Home Page I K JJII JI 120 30 w 4 y f x pm x K uF g x h x df x g x h x g x h x f x u x pm x u x ef x g x y ef x g x pm x g x Kp x h x l pm x hm x f x hm x f x pk1 1 x pk2 2 x pks s x p1 x p2 x ps x X 1 p eys 1 K s 1 K u g x pk1 1 x h x pk2 2 x pks s x kf x g x h x f x g x u m f x hm x g s 1 SNJ K Home Page I K JJII JI 121 30 w 4 2 y A 5y g X 10 m f x x 1 2m x2m 2x 1 K x x 1 2x 1 f x y x x 1 2x 1 p Iy x f x x 1 f x 2x 1 f x yd Iy f 0 f 1 f 1 2 0 f 0 1 1 0 f 1 02m 1 2m 2 1 1 0 f 1 2 1 2 2m 1 2 2m 2 1 2 1 0 SNJ K Home Page I K JJII JI 122 30 w 4 x f x x 1 f x 2x 1 f x l x x 1 2x 1 f x 3 u 11 y xn axn m b Uk u2 y f x xn axn m b K f 0 x nxn 1 a n m xn m 1 y Iy f 0 x Uk f 0 x xn m 1 nxm a n m xn m 1q x q x nxm a n m q0 x nmxm 1 q0 x q x of 0 x l f x 2 SNJ K Home Page I K JJII JI 123 30 w 4 4 n5y K8 12 ef x 6 0 f x f xn Kf x U 0 y ef x k duf x f xn f xn f x q x Kf n f q 0 l n f x n n n 2 nk f x d n f x kk o 7k n j n k j k K n j n k nj 1 0 k n j 0 n k nj 1 0 5 Eisenstein O 13 y f x xp px 1 p 3kn Q SNJ K Home Page I K JJII JI 124 30 w 4 y C x y 1 K f x y 1 p p y 1 1 yp C1 pyp 1 Cp 2 p y2 Cp 1 p p y p 3 p 1 p 1 2 p U X 3 p2 p dEisenstein O 14 f x 1 x x2 x3 x4 x5 x6 1 f x L ux 1 2 yf x 3 S 1 dn f x x 1 6 7 x 1 5 21 x 1 4 35 x 1 3 35 x 1 2 21 x 1 7 2 y x 1 K f x y6 2y5 21y4 35y3 35y2 21y 7 p 7 KdEisenstein O f x 3kn f x f 0 x 1 of x 3 l f x 3 SNJ K Home Page I K JJII JI 125 30 w 4 6 y 5y K8 15 f x x3 ax2 bx c X ac bc yf x 3kn Q y bef x 3kn Q Kf x 3 Z qdegf x 3 f x 7k g l x3 ax2 bx c x p x2 qx r p q r Z u pr c duac bc a b c a b c p r u f 1 1 a b c f 1 1 p 1 q r g l f x 3kn Q SNJ K Home Page I K JJII JI 126 30 w 4 16 3kn Q y ng f x x a1 x a2 x an 1 ai i 1 2 n p y y bef x 3kn Q K 3 Z 3 X h x g x f x h x g x max degg x degh x n f ai 1 f ai h ai g ai 1 l g ai h ai 1 s x h x g x Ks ai 0 i 1 2 n es x 6 0 K degs x max degg x degh x n a1 a2 an s x n p n8g SNJ K Home Page I K JJII JI 127 30 w 4 s x 0 h x g x l f x g2 x f x X 1 g f x 3kn Q 17 f x x a1 x an 1 a1 a2 an p y f x 3 kn Q f x X y w f x X 3kn Q o 3 f x g n X f x g x h x f ai 1 i 1 2 n g ai h ai 1 1 g ai h ai qmax degg x degh x n od n9 g x h x f x g2 x SNJ K Home Page I K JJII JI 128 30 w 4 5y 18 m x f x g x XJ 1 f x m x g x m x 2 f x g x m x f x g x L f x g x X 1 y XJf x g x X 1 o f x g x f x g x f x g x y f x g x d x f x d x f1 x g x d x g1 x K f x g1 x g x f1 x f x g1 x f x g x SNJ K Home Page I K JJII JI 129 30 w 4 g h x f x g x h x f x s x h x g x t x K d x f1 x s x d x g1 x t