# At a Glance - Multivariable Polynomials

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 where each term looks 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 don't qualify as polynomials in the first place.

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

• x2 + 2y is not a polynomial because it's using a variable as an exponent. Tsk tsk.

• xy2xy(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 + xyy

#### 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:

πx2 + 3.4xy4 + x2y5 – 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:

5xyy7 + x - 4y4