X goila idean nguyen t6 ngu• va chi lieu veil u, u E tich
2) Ala trubng cac s6 nguyan mod
—1x3 — 7x2 + ix — 4 -aX2 aX - - Tx3 + 1x2 - 5x 6x + 4 - Tx3 + 1x2 - 5x 6x + 4 -8X2 aX - g -8X2 gX - g 0 Vay —1 — 7x2 2x — 4 = (-2x2 + 2x — 1)(6x + 4)
• Tit (hob nghia 2 (ch III, §1, 2) va djnh 11 . 3 ta co the khAc ha qua.
H. qua. f(x) chia hit cho g(x) khi va chi *hi du trong phep chin f(x) cho g(x) bang 0.
4. NghiOm cga mOt da thtic
Dinh nghia 3. GM si c la mOt phan tit tag g eim vanh A, /la/ = an 4- apc + + ani la mOt da thlic thy 3, cim vanh
Aix] ; phiin tit
f(c) = an + a i c + + ane e A
dttqc bang each thay x bai c goi la gin tri caa f(x) tai c. Ngu f(c) = 0 thi c goi la nghigm caa f(x) Tim nghiem ciut f(x) trong A goi la gidi phuong trinh dui s6 b4c tt
ant + + an L-- 0 (an * trong A.
Dinh H 4. Gid sit A la mdt &yang, c E A, f(x) E Aix]. The
can pile)) chia f(x) cho x - c In f(c).
Ching mink. Ngu ta chia f(x) cho x - c, du hoac bang 0 hoac la mat da tilde bac 0 vi bac (x - c) bang 1. Slay du la mat phan tii r E A. Ta cd
f(x) = (x - c) q(x) + r Thay x bang c, to dupe
f(c) = 0 q(c) + r,
vfly r = f(c). n
HO quA. c la nghiqm caa f(x) khi vet chi khi f(x) chin hit cho x - c.
Thqc Man phep chia
f(x) = anx" + 1 + + an
cho c, ta dude cac he td cua da tilde thing
q(x) = b oxn i + b izji 2 + + n _
cho belt cac cOng flute
b o = ao, bi = + cbi - 1
va du
r = an + _ 1 .
Vi r = f(c), ta say ra mat pluming phdp (phuong plulp Hoocne) dg tinh f(c) bang so dc" eau day :
a a, a
chb 0 n -1
trong do rani phan to taa clang thd nhi doge bang each cOng
vao phan tit taring ang mla ding thil nit& tich cita c voi phan
to dilng trot& clang tht? nhi.
Dinh nghia 4. Gia sit A la mat tniang, c E A, fix) E Aix] va m la mat ea to nhien 1, c IA nghiem bei cap m nau va chi nal' f(x) chia hat cho (x - cfn va f(x) khOng chia hgt cho (x - Trong trUang hop m = 1 noted ta can goi c IA nghiem don, In = 2 thi c la nghiem Jeep.
Ngtted ta coi mat da thttc ea mat nghiem bed cap m nhu mat
da thole c6 m nghigm trimg vai nhau.