Question
Wed February 20, 2008 By: Shikha Mukhi

find r(X) when p(x) is divided by (x-2)(x-3).r(x)=1 when g(x)=(x-2) and r(x)=3 when g(x)=(x-3)

Expert Reply
Thu February 21, 2008

Find r(X) when p(x) is divided by (x-2)(x-3).r(x)=1 when g(x)=(x-2) and r(x)=3 when g(x)=(x-3)
Query Description:

a polynomial p(x) gives remainder 1 when divided by (x-2) and remainder 3 when divided by (x-3). what will be the remainder when p(x) is divided by (x-2)(x-3).

Let the remainder when P(x) is divided by (x-2)(x-3) be ax+b
Using Division Algorithm we have p(x) = (x-2)(x-3) q(x)+(ax+b)-------(1)
Now p(2) =1 P(3) =3 given 
substituting x =2 and x =3 in (1) we have 
1= 2a+b
3=3a+b
Solving we get a =2 and b =-3
So the remaninder is 2x-3

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