# What is a polynomial?

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 .

## Is it a polynomial?

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)