The conversation between human and AI assistant.
How do I show that polynomial [math]p(x)=\frac {p(x+1) + p (x-1)}{2}[/math] has degree atmost 1?
Right. And then what?
Now, let's assume that [math]p(x)[/math] has degree [math]n[/math], meaning that the highest degree term in [math]p(x)[/math] is [math]x^n[/math]. Then, we can write [math]p(x+1)[/math] and [math]p(x-1)[/math] as [math](x+1)^n[/math] and [math](x-1)^n[/math], respectively.