__maths__>__Introduction to Algebra, Polynomials, and Identities__>__Polynomials - Basics__### Variables in a Polynomial

Based on the number of variables in a polynomial, the polynomial is classified as polynomial of n variables.

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The price of a pencil is `3` coins and a pen is `7` coins. For how many coins does a person buy `x` pencils and `y` pens?

- `3x+7y`
- `3x+7y`
- `(3+7)xy`

The answer is '`3x+7y`'. *An expression can have more than one variable.*

How many variables are there in the polynomial `x^7-.3x^5+.67x^2-3`?

- `1`
- `1`
- `4`

The answer is '`1`'. This is an example of *polynomial of one variable*.

How many variables are there in the polynomial `x^2-y^2+xy`?

- `3`
- `2`
- `2`

The answer is '`2`'. This is an example of *polynomial of two variables*.

How many variables are there in the polynomial `3`?

- `3`
- none
- none

The answer is 'none'. This can be considered as *a polynomial without a variable*.

Based on number of variables polynomials are classified as polynomial of `1` variable, polynomial of `2` variables, etc.

**Classification of Polynomials Based on number of Variables:**

• Polynomial of no variables : a constant. eg: `4`

• Polynomial of `1` variable. eg: `4x^5+x^2-3`

• Polynomial of `2` variables. eg: `3.2x^5y^2+.23xy-3x^2+y-9`.

And polynomials of `n` variables.

*Solved Exercise Problem: *

How many variables are there in the polynomial `x^2-y^2+z^2+xyz+2xy-2yz+3xz`?

- `3`
- `3`
- `2`

The answer is '`3`'. This is an example of polynomial of `3` variables.

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