- Topics At a Glance
- Exponents
- Negative Exponents
- Fractional Exponents
- Irrational Exponents
- Variables as Exponents
**Defining Polynomials**- Degrees of a Polynomial
**Multivariable Polynomials**- Degrees of Multivariable Polynomials
- Special Kinds of Polynomials
- Evaluating Polynomials
- Roots of a Polynomial
- Combining Polynomials
- Multiplying Polynomials
- Multiplication of a Monomial and a Polynomial
- Multiplication of Two Binomials
- Special Cases of Binomial Multiplication
- General Multiplication of Polynomials
- We'll Divide Polynomials Later!
- Factoring Polynomials
- The Greatest Common Factor
- Recognizing Products
- Trial and Error
- Factoring by Grouping
- Summary
- Introduction to Polynomial Equations
- Solving Polynomial Equations
- In the Real World
- I Like Abstract Stuff; Why Should I Care?
- How to Solve a Math Problem

We can also have polynomials with more than one variable, called **multivariable polynomials**. They're like multivitamins, but even better for you. A multivariable polynomial is a finite sum of terms that look like this:

(real #)(first variable)^{(first whole #)}(second variable)^{(second whole #)}…(last variable)^{(last whole #)}

Not every variable needs to appear in every term. Some of them probably won't, since they were out partying late last night.

The following are multivariable polynomials.

*xy*

- 5
*x*+ 2y^{2}

- 3
*x*^{2}+ 2*xy*^{2}– 4.5*x*^{2}*y*+*y*+ 2

The following all have multiple variables but are not multivariable polynomials, because they do not qualify as polynomials in the first place.

- is not a polynomial because dividing by a variable is not allowed in a polynomial.

*x*^{2}+ 2^{y}is not a polynomial because it's using a variable as an exponent. Tsk tsk.

*xy*^{2}–*xy*^{(0.5)}is not a polynomial because the exponent (0.5) is not a whole number. For example, you can't have 2.5 children, even if that is the national average.

Exercise 1

Is the following expression a multivariable polynomial? If not, explain why:

*x* + *xy* - *y*

Exercise 2

Is the following expression a multivariable polynomial? If not, explain why:

Exercise 3

Is the following expression a multivariable polynomial? If not, explain why:

π*x*^{2} + 3.4*xy*^{4} + *x*^{2}*y*^{5} - 11

Exercise 4

Is the following expression a multivariable polynomial? If not, explain why:

*x* + *y* + 9^{(-1)}

Exercise 5

Is the following expression a multivariable polynomial? If not, explain why:

5*xy* - *y*^{7} + *x*^{ - 4}*y*^{4}