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find r(X) when p(x) is divided by (x2)(x3).r(x)=1 when g(x)=(x2) and r(x)=3 when g(x)=(x3)
Find r(X) when p(x) is divided by (x2)(x3).r(x)=1 when g(x)=(x2) and r(x)=3 when g(x)=(x3) 
Query Description: 
a polynomial p(x) gives remainder 1 when divided by (x2) and remainder 3 when divided by (x3). what will be the remainder when p(x) is divided by (x2)(x3). 
Let the remainder when P(x) is divided by (x2)(x3) be ax+b
Using Division Algorithm we have p(x) = (x2)(x3) 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 2x3