By "general" I mean a formula that describes all polynomials using letters to represent coefficients and powers. For example, the "general" term for a quadratic is $ax^{2}+bx+c$, the "general" term for a 2-dimensional vector $\overrightarrow{v}$ is $\left[\begin{array}{} {v_1} \\ {v_2} \\ \end{array}\right]$, just so you understand what I mean by "general".
Now, my question is: Is there a general way to refer to polynomials? I've seen before $a_{1}x^{n}+a_2x^{n-1}+a_3x^{n-2}\cdots +a_nx^{0}$ ,but it seems overly redundant, it's a little hard to look at, and the "..." can be confusing and misleading at times. Is there a better way to represent this? Thanks in advance!