Question

Polynomial P(x) contains only terms of odd degree. When P(x) is divided by x-3, the remainder is 6. What is the remainder when P(x) is divided by x^2-9

Answer 1

Look at the simplest case where P(x) = ax,
Then
ax/x-3 = a+ 3a/x-3
remainder = 3a = 6 --> a = 2

Then
2x/(x^2-9) --> remainder is just 2x