Also, From Wikipedia
When writing polynomials, the coefficients are usually taken to be known and the indeterminates to be unknown, but depending on the problem, all variables may assume either role.
Isn't it is the case that coefficients are constants and not variable? What it is referring towards by 'inderminates'-variable?
Is it related to dependent variable and independent variable?
On
This mainly has to do with certain (quite vague) conventions in calculus.
In particular, if a test asks you to compute $$\frac{d}{dx}(ax^2),$$ the person marking the test probably wants to see $2ax$, not $$\frac{da}{dx}x^2+2ax.$$ That's because you're meant to treat $\frac{da}{dx}$ as being equal to zero, the intuitive explanation being that $a$ is "held constant" while $x$ varies.
(Unfortunately, this is never really made precise or rigorous.)
Here's an example of how it might be the other way around - I want to model a particular set of data with a cubic function. So I have a set like $(1, 7), (2, 5), (3, 7), (4, 19)$, etc., and a function $y = a_0 + a_1 x + a_2 x^2 + a_3 x^3$. In this context, the $x$ and $y$ values are known, and the coefficients $a_0$ up to $a_3$ are unknown. What's more, by specifying a different data set (or even a different model), those coefficients can vary. And if they vary, then presumably they are variables.