The expression is excatly divisible by . When is divided by , the remainder is 8 more than when it is divided by . Factorise completely.
If x divides f(x) thenis excatly divisible by .
leaves no remainder. Thus
This gives a remainder of c, but f(x) is divisible by x, thus c = 0.
You can do this quicker by using the fact that if f(x) is divisible by x - r then f(r) = 0. In this case r = 0, so f(0) = 0.
-Dan