ร8-64

( )p x an xn + an−1xn−1 + an−2 xn−2 + ... + a1x + a0 = 0

n an , an−1, an−2 ,...,a1, a0 an  0

p(x) x − c c

p(c)

1

x2 − x +3 x + 2

(− 2) p(x) =p(xpx22()x−=)x=xp2+(xx−32)x−=+xx3+2 −3 x + 3
p(− 2p)==(=ppppp−pppp94(((((2(((−−−−−−xxxx+x9)22222)))2===−2p)))))====29========4==2c===(+=−xxxx−+9999x44449943(((((22222−−−−−(−2+++++xxxxx9999−−−−−9)222222==cp+−−−−=−222222xxxxp)))))−(2222x293cccc4)++++c(−+(++++−x+(−−−−−++3333x−3293333)23((((()2=−22−−−−−)===x2)c+x22222+94−+(xxxx2xp))))3)−3+++++(x+(9−++++2+x−2−233333)x2222)2x22c++px)−−(+3+3pppppx((−(((3()−2xxxxxx2)))2)−xxxxxx)x)p+(−−−−−++−(2((((x(322−−−−−)xx)22222+xxxxx−)))))p++++2+((−x22222)2xx
x+2

2

x−(x7+−3(1−−21+x)3)1=2=xx)+22−p0−p(7(+3−x((xx−−7)1−−1122)=xc24))03−2−==x3222pp72pp40((((−(−−−−xxx1p11pp17+)1−x))0)(0)((2)0x3=−=1−=−+c=4==2=3+111212p−x022+px2)0p00())(p0(x04(−((=−x(7=+x=x−x=p−(x=x4=x−−1()1−2(21)1−p)1−0−p−)22p)xpp=x0170x())c2+==(4(()cc(1(−(x440(xx−7+−x−−x2+x−=x)72=x2−3)1−−1xx3xx)11−1)1−(x7x)7x=2+)+p2030)−7c)4+7=+4)+=(4(c(−44c=(41x=(−−(−x+21−x1−2x1−(x−−2−x2−34)−x1x2−)x1−12px0x7+17xxpx+1x7))+)(=−47(7+++c17)44+x3−(x)2(−41x−x431−1(x3)−2(x213x7−1+−7x)12−−1x32+−−3+2−x3()1xx+x)+=7x+xx27−++1−(c+7x4)2147+47(+72−+34(x3(x)−−11x1)p24x−−−xx(3px−2x7xx1x3314−x++)p12(−1x4332−12(32()1x7+47x3+−+72+()−xx24)2+−7(−x1x)+x2+(x)+4xx372−−x+1x)1(2+x2−3−x−)+7(xp412x)27−3+−74+−x37x−1xx−4x3px+71)2(xx7p(x7−+7+x+321)(−x4+7x(2)−71−2(4−+x3x4−−22+((x−(73x3)−xx1)(+7x)p−−−−xx7x3+172++x−2x−−x−3(3+7112++4x+−)(72(3)x−)31x132+−x)−xx)+7x1++72x7−7−x+x72x(x2+7(33)7x)x+1))423−+−x−3x11+(2xxx−x7(−x+7−x−2p)(−x+77−−−−3)++31+1x−74(2+33−x2(−−73(+x(7(3−3−))+11x(+x−27−x3−7x−1++xx2+(xx−73−3)3)()71−231x+)+xx−1−12−2px+7x−x−17−7)3x)x132)+)(−)72xx3x+−1+−(xx−)733−2−−(++−−)32−x7−+−(3−3−771+(3−371++x(xx3−−)1(x7x3−3)x12−7)7+−x1x3x−)−1−1+xx)2−1−3)−)3x33x−−7+3(3+x+x−33711−+1xp)x13−(−+xx3

0 x +1 2x4 − 7x3 + x2 + 7x − 3

33333333 3 3 ( ) ( )3333ppppp3(p(pp(((ppxp3pxxxxxx(xxpx)(p)(px23)−)p23xx−2323=x−−23x−=x==)=(p)=c23)−=c=23x===cc=−==236==−c====x6========6======6=)===c=x93=2332=xc−9===26cx399336=33226====x=9663832=6=6=8=666=8826=28=226=cx93322=6x=9=34332x−9633432=−683443−−−6694−=94−4389−29468p326p−63292463226x9332236643233−233223338(−x4369x−4p34xpx−x2−332−x−9−−49234x6xx−xx23x−632x−6+2−+2342+−22x2233+x+2p+−−94x2+23)3233x2−+x23x6−x−23x−−−−−−x−(−2323−3−332p131=−32+−3123xx−2+−x−−+2233+2x1=x2−2++23x32=22c2−x=−−+=2x=23x−x−−23226)3+1−=−c−3−32233=x13+1++3232=−=6−=−32+=2x329+3−++33223=1p32p326p22x111++++86xpx=cx92+1322322+=((116==1++32326x=+++8(111x61x=43pp−x+++12−239+pp+41x11x93++3232)+)116(p(11p1348−((+1612)33+1−1x924xx++1(1−xx1x236+x143x)−−1+2)−)9+)4c2c3311cx3223−6)x1−c−−=2323331x==−x33+2x=−23+=cc=322x3=cc−==xx+262=c−+x−=3232−cc23+332x1=323−c=−−=−x39323332233c1=p6−31232+8==−x6x32xx=2(322xc=32x32+c2+1c23x3243−c−2+−233232−−9423+−)p=231+321=p+=321=+2233222x1(1−+32+1x1xx3232c−+2+)11−=−3231322c32cc+32==3p=13+x(2332cx+1x−32c)=1−2=232pppcp32p2323=32ppp3223p23c32232332=

2 p 2 
3 3

4

p(x) = x3 + 2x + 7 x−3 p(3)

x−c x−3

p(x)

p(3) = (3)3 + 2(3)+ 7

= 27 + 6 + 7

= 40
40

1. p(x) = x4 − 3x + 5 x−2
2. p(x) = 3x3 − x2 + 4x − 2 x +1

3. p(x) = 2x4 − 5x3 − x2 + 3x +1 x+ 1
4. p(x) = 2x4 − 3x2 + x −1 2

2x + 3