1.若多項是f(x)分別以x-1,x-2,x-3除之,餘式依次為5,10,17,則f(x)除以(x-1)(x-2)(x-3)的餘式為何? 2.設三次多項式f(x),以,x2+X+2除之得餘式x+2,以x2+x-2除之得餘式5x-2,求f(x)? (※X2是x平方) 國中 回應 lochihsin Re: 餘式定理因式定理-怎麼算 2009-12-28 17:16 1.令f(x)=(x-1)(x-2)(x-3)q(x)+a(x-2)(x-3)+b(x-3)+17 f(1)=5=2a - 2b+17 f(2)=10= - b+17 b=7 a=1 f(x)除以(x-1)(x-2)(x-3)的餘式=(x-2)(x-3)+7(x-3)+17 2.令f(x)=(ax+b)(x^2+x+2)+x+2 x2+x-2=(x-1)(x+2) f(-2)= - 12 f(1)=3 a=1 b= - 1 f(x)=(x-1)(x^2+x+2)+x+2 (※X^2是x平方)
lochihsin Re: 餘式定理因式定理-怎麼算 2009-12-28 17:16 1.令f(x)=(x-1)(x-2)(x-3)q(x)+a(x-2)(x-3)+b(x-3)+17 f(1)=5=2a - 2b+17 f(2)=10= - b+17 b=7 a=1 f(x)除以(x-1)(x-2)(x-3)的餘式=(x-2)(x-3)+7(x-3)+17 2.令f(x)=(ax+b)(x^2+x+2)+x+2 x2+x-2=(x-1)(x+2) f(-2)= - 12 f(1)=3 a=1 b= - 1 f(x)=(x-1)(x^2+x+2)+x+2 (※X^2是x平方)
回應
lochihsin
Re: 餘式定理因式定理-怎麼算
2009-12-28 17:16f(1)=5=2a - 2b+17
f(2)=10= - b+17
b=7 a=1
f(x)除以(x-1)(x-2)(x-3)的餘式=(x-2)(x-3)+7(x-3)+17
2.令f(x)=(ax+b)(x^2+x+2)+x+2
x2+x-2=(x-1)(x+2)
f(-2)= - 12 f(1)=3
a=1 b= - 1
f(x)=(x-1)(x^2+x+2)+x+2
(※X^2是x平方)