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
   
• 5x + 2y²
   
• 3x² + 2xy² – 4.5x²y + 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.
   
• x² + 2^y is not a polynomial because it's using a variable as an exponent. Tsk tsk.
   
• xy² – 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.

Multivariable Polynomials Practice: