Hello,

p(x)=(x-2)Q(x)+1

p(x)=(x-3)R(x)+3

thus we know that p(2)=1 and p(3)=3

Let s(x) be the remainder of p when divided by (x-2)(x-3)

p(x)=(x-2)(x-3)T(x)+s(x)

Since (x-2)(x-3) is of degree 2, s(x) has to be of degree 0 or 1.

Substituting x=2 and x=3, this gives the system :

So we're looking for and such that and

Substitute :

You can finish it eh ?