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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?

Martin Sleziak
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ankit
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    Well, what are constants? Are they really anything other than variables that we are thinking of as not changing? :) – Caleb Stanford Sep 15 '16 at 05:32
  • Yes, constants represents fixed numbers whose values are not changing in an expression. – ankit Sep 15 '16 at 05:39
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    What does "values are not changing" mean? As far as I know, there is no formal difference between a constant and a variable. – Caleb Stanford Sep 15 '16 at 05:47
  • A variable is a symbol that can take many/all values in an expression from the given values but a symbol representing constant can take only one value among the given values it can hold. – ankit Sep 16 '16 at 03:25

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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.

ConMan
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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.)

goblin GONE
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