A polynomial p(X) of degree more than 2 has a remainder of 9 when divided by (X+2) and a remainder of -1 when divided by (x-3),find p(X)
This question does not have a unique solution as it stands.
I have already found two cubic equations that satisfy the given conditions.
p1(x) = x^3 - 4x^2 - 5x + 23
p2(x) = x^3 +x^2 - 10x - 7
Both p1(x) and p2(x) divided by (x+2) leave a remainder of 9, and
Both p1(x) and p2(x) divided by (x-3) leave a remainder of -1.