Hello, My problem is the same as osnarf's problem in thread "Polynomial division proof", https://www.physicsforums.com/threads/polynomial-division-proof.451991/ But, I would like some further help. The problem: Prove that for any polynomial function f, and any number a, there is a polynomial function g, and a number b, such that f(x) = (x - a)*g(x) + b for all x. After some steps a) n=1, f(x) = ax+a=a(x-a)+(a+aa) b) Suppose it is true for n=k, f(x)= a[k]x[k]+ a[k-1]x[k-1] +...+ ax+a f(x)=(x-a)g(x) + b c) n=k+1 : f(x) = a[k+1]x[k+1]+ a[k]x[k] +...+ ax+a and since we have supposed that f(x) is true for n= k, it turns into a new polynomial : h(x) = f(x) - a[k+1](x-a) and has degree <=k? I understand f(x), but a[k+1](x-a) is it correct? Did it come from a[k+1]x[k+1]? thanks Sorry for any inconvenience on reading this thread.