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A polynomial is an expression which consists of variables, constants and exponents joined using addition, multiplication, and subtraction. Example:

x^2 + 5*x + 9 is a polynomial

By the definition, both linear and quadratic functions can be considered polynomials.

When we have negative or fractions for exponents, or letters under a radical, an expression cannot be considered as a polynomial. Example

1/(X-1) + 6*X^2 is not a polynominal

Consider the polynomial:

X^4 + 9X^3 - 2X^2 + 2

The degree of a polyniminal is the highest exponent so in above polynomial, the degree of the polynomial is 4.

The degree of the term is the exponent to which the variable in the term is raised. In the example above there are four terms of degree 4, 3, 2 and 0 (the constant term has degree 0).

Please let me know if you need any clarification. I'm always happy to answer your questions.