Question

整式P(x)除以x-2得到的余数是-1x+3得到的余数是9,求P(x)除以(x-2)(x+3)得到

Answer 1

P(x)=Q(x)(x-2)(x+3)+ (ax+b)

P(x)除以(x-2)得到的余数是-1 

P(2)=-1

2a+b=-1                                               (1)

P(x)除以(x+3)得到的余数是9

P(-3)= 9

-3a+b=9                                               (2)

(1)-(2)

5a=-10

a=-2

from (1)

2a+b=-1  

-4+b=-1

b=3

(a,b) =(-2,3)

P(x)除以(x-2)(x+3) 的余数是 = ax+b = -2x+3