p(x) is a polynomial of degree>2. When p(x) is divided by x-2, it leaves remainder 1, and when divided by x-3, leaves rem. 3. Find the remainder when p(x) is divided by (x-2)(x-3)
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 ?