Question

余式定理的题 若以2x^2-3x-2除多项式f(x)与g(x),分别得余式2x+3与4x-1,则以2x+1除f(x)-g

Answer 1

f(x)=a(2x^2-3x-2)+2x+3

=a(2x=1)(x-2)+2x+3

g(x)=a(2x^2-3x-2)+4x-1

=a(2x=1)(x-2)+4x-1

a能整除

所以

只要算 (2x+3)/(2x+1)=1.2

(4x-1)/(2x+1)=2.-3

answer is 2-(-3)=5