Indeterminate (variable)

In mathematics, and particularly in formal algebra, an indeterminate is a symbol that is treated as a variable, but does not stand for anything else but itself and is used as a placeholder in objects such as polynomials and formal power series. In particular it does not designate a constant or a parameter of the problem, it is not an unknown that could be solved for, and it is not a variable designating a function argument or being summed or integrated over; it is not any type of bound variable.

A polynomial in an indeterminate X is an expression of the form ${\displaystyle a_{0}+a_{1}X+a_{2}X^{2}+\ldots +a_{n}X^{n}}$, where the a_i are called the coefficients of the polynomial. Two such polynomials are equal only if the corresponding coefficients are equal. In contrast, two polynomial functions in a variable x may be equal or not depending on the value of x.

For example, the functions

are equal when x=3 and not equal otherwise. But the two polynomials

are unequal since 2 does not equal 5 and 3 does not equal 2. In fact

does not hold unless a = 2 and b = 3. This is because X is not, and does not designate, a number.

...
Wikipedia