- 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

When finding the degree of a multivariable polynomial, remember to keep your head above ground. That goes for any ostriches who may be reading this. Ignore the constants and look for the exponents hovering in superscript. To find the degree of a multivariable term, add together the exponents of all the variables in that term. Isn't it nice to be asked to *add* once in a while?

- The degree of the term
*xy*is 2, since each variable has an exponent of 1. They are invisible, but they are there...watching you step into the shower. Creepy.

- The degree of the term 34
*x*^{2}y^{3}is 5. To find this sum, we add together the exponent of*x*, which is 2, and the exponent of*y*, which is 3. Similarly, Kevin*x*^{2}Bacon^{4}would give us the 6 degrees of Kevin Bacon.

- The degree of the term 45
*x*^{6}y is 7. This is the sum of the exponent 6 from the*x*and the exponent 1 from the*y*. We could give you another half dozen examples, but we think you have this adding thing down pat.

You already know that the degree of a polynomial is the largest degree of any of its terms. Well, guess what? The same is true for multivariable polynomials. To see which term has the largest degree, we need to find the degree of each of the terms and then pick the biggest number. "Picking the biggest of something" is about the only thing easier than adding, so you should have no problems here.

Example 1

What is the degree of the multivariable polynomial 4 |

Example 2

Determine the degree of each term of the polynomial 5 |

Exercise 1

Determine the degree of the following polynomial: 23*x*^{4}y^{5} + 17*x*^{3}*y* - *x*^{8} + *xy*^{9}

Exercise 2

Determine the degree of the following polynomial: 5*x*^{10}*y* + 11*x*^{2}*y*^{5} + 3*x^{5}y^{3}*

Exercise 3

Determine the degree of the following polynomial: 3*x*^{20}y^{10} - 6*x*^{17}y^{13} - 45*x*^{19}y^{11}