It is clear that g must be a polynomial of degree no more than 1 higher than the degree of f (because the highest power of g(x) will cancel in "g(x)- g(x- 1)) . If f(x)= 2x- 1 then you can write . The condition that tells you that c= 0. So for all x. In order that two polynomials be the same for all x, they must have corresponding coefficients the same: 2a= 2 and b- a= -1. 2a= 2 gives a= 1 and then b- a= b- 1= -1 gives b= 0.