Try this problem from TOMATO Objective 288, useful for ISI BStat, BMath Entrance Exam based on finding big remainder in a small way.
Problem: Tomato objective 288
The remainder R(x) obtained by dividing the polynomial by the polynomial is
The the divisor is a quadratic term .So, R(x) must be 1 degree less than divisor.
We know ,
solving two equation we get,
The remainder R(x) is