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.
- 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.
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:
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:
5xy – y7 + x - 4y4