Question

How to know that it is in one variable or not?

Answer 1

In order to find out whether a polynomial is in one variable or not, just check whether the polynomial has only one type of variable.

For example,

x^2 - 3x - 4x is a polynomial in one variable because there is only 1 type of variable x.  z^5 + y^10 + x^9 is not a polynomial in one variable because three different variables x, y and z are present.

Also make sure that the exponent is a whole number for the variable.

For example $\sqrt{t}$ is not a polynomial in one variable because the exponent of t is 1/2 which is not a whole number.