Is $p(x) = x$ a polynomial?

Question

Let $p(x) = x$ for all $x \in\Bbb R$ . Is $p$ a polynomial?

I'm not sure how to prove it. Does it have to do with the degree of the function?

Answer 1

A polynomial of degree $n$ is any function that can be written as: $$a_0+a_1x+\cdots + a_nx^n$$

Your function here fits that definition, with $n=1$, $a_0=0$ and $a_1=1$.