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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.

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