7(1-73)
_-61J6²-496
除去
1-2-2
= -2
2
X-2X+1=3 5-24-220
5 +440
好學範例4 除式二次的餘式「412
= -22 +22/3-11
= -33 +2253 #7
2006+12+12
-10 + 1
設多項式 f(x) 除以x² - 5x + 4,餘式為 x+2;除以²-5.x + 6,餘式為 3.x + 4,則多項式
f(x) 除以 x² - 4x + 3,餘式為
XX-2
學測
解析 f(x)=X-SX+4 = [(x+2> f(x)=(x+1)(51) 975) +X+2
解題關鍵
f(x)=x-sk+l=900x14 ) f(x)=a-3)(4-head() 出除法原理設
f(x) = x² - 4x + 3 = 9(x)-. ? -
f(x) = (x² - 4x + 3)Q(x) + (ax + b)。
X²³-5x+4 = (x-4) (x-1) ·x²4x-15 = (x-3)(x-1)
(2) 令除式(?-4x+3) = 0 → x = 1或3
X -4
代入求餘式。
*- 3
X-1
x-1
> 設f(x) = (43) (81) 9(0) +(ax+b)
X-=-X
-3X-X=-4X
²-x+6 = (X-3)(x-2)
(XxX=1-3/1²/1
a+b=3²²
X-S
9 = 56 = -2
X-2
3a+b = 13
-3x-2x=√x
-22 (1-3) -1^
{ sto
5X-24
19
