F₁²) = c+5 = 5 c = 0
a=2
★ 搭配講
範例 14
求餘式
設(x)為一多項式,已知(x-1)f(x)除以(?-2x+2的餘式為3x+4,則f(x)除以7-2
餘式為
O
1=9 1 = $+0+99+ (17)
O
Y(x)
a
解題提示 先用除法原理假設f(x)=(xx-2x+2)g(x)+(ax+b),再放大被除式
f(x)
f(x) = g(x)q(lx) + √(x) 7
gix) · gix) + gox) x²1x) (x²+ (b-a) x-b
陈式2次,餘式多以
Ax - 2ax +2a
(x-1) f(x) = (x-1) (x²-2x+2) qux) + (3x+4)
(x-₁) f(x) = (x+) (x²2x+2)q(x) + ax+b (x+)
(ax+bx++)
(x+) f(x)
x²=2x +2 = (x-1) g(x) + x²=2x+Z
= (x-1) qu(x) + ax + (b-a) x-b
x=2x+2
(b-2a) x--6-29
b-2a=3x
L-b-za=4
(x+ks
sacrif
(b-2ax-b-za
x-2x12
= [(x-1)qm)+a] +
-7x+10