A polynomial is an algebraic expression involving many terms and can be factorised using long division or synthetic division.

A polynomial is a chain of algebraic terms with various values of powers. There are some words and phrases to look out for when you're dealing with polynomials:

**variable**- The part of an expression that can have a changing value. In the variable is**co-efficient**- The number before a variable showing how much it is multiplied by. In , and are co-efficients**index**- The power of a variable. In , the of and the of are indices (plural of index)**degree**- The**index**of the**highest power**. In the degree is**constant**- A number that does not contain the variable. In , the constant is

is a polynomial in of degree .

is a polynomial in of degree .

For the expression to be a polynomial the index of any variable must be a positive whole number

- Question
Is a polynomial?

No. is not a polynomial.

Another way of writing is as .

This index is a fraction not a whole number. That is why this is not a polynomial.

- Question
Is a polynomial?

No. is not a polynomial.

Another way of writing is .

This index is negative not a positive whole number, so this is not a polynomial.

- For an expression to be a polynomial every index must be a positive whole number.
- There cannot be any roots of a variable (this would be a fractional index)
- There cannot be any variable in the denominator of a fraction (this would be a negative index)