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)

Asked by shikha | 20th Feb, 2008, 10:14: PM

Expert Answer:

 

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

Answered by  | 4th Dec, 2017, 03:08: PM

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