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How do I show that polynomial [math]p(x)=\frac {p(x+1) + p (x-1)}{2}[/math] has degree atmost 1?
I need to show that the polynomial [math]p(x)=\frac {p(x+1) + p (x-1)}{2}[/math] has degree at most 1.
Okay, let's start by expanding the expression. [math]p(x)=\frac {p(x+1) + p (x-1)}{2}[/math]  can be rewritten as [math]p(x)=\frac{1}{2}p(x+1) + \frac{1}{2}p(x-1)[/math].