Intro to Polynomials

A polynomial is an expression involving a sum of powers in one or more variables multiplied by coefficients, where the powers must be whole.

 $\sqrt{x}$  is a non-whole number exponent.
 $x^{-2}$  and  $x^{-1}$  are non-whole number exponents. 

A polynomial can be classified by the number of terms it has. Each term of a polynomial is separated by addition or subtraction.

The degree of a polynomial is the highest exponent or the sum of exponents on any variable term.

Polynomials in standard form have the highest degree variable term followed by descending powers of the variable terms.

How can we classify this polynomial?

For multivariable terms, there can be multiple standard forms for the polynomial.

The top example is in descending powers of x, while the bottom example is in descending powers of y. Both examples are fourth degree polynomials in standard form.

Simplify the polynomial by combining like terms, and write the polynomial in standard form. Classify the polynomial by number of terms and degree.