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Polynomials

Polynomials

At a Glance - Degrees of Multivariable Polynomials


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?

Sample Problems

  • The degree of the term xy is 2, since each variable has an exponent of 1. They're invisible, but they're still there...watching you step into the shower. Creepy.
     
  • The degree of the term 34x2y3 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, Kevinx2 Bacon4 would give us the 6 degrees of Kevin Bacon.
     
  • The degree of the term 45x6y 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's the degree of the following multivariable polynomial?

4x2 + 3x2y – 5xy4 +7y – 9


Example 2

Determine the degree of each term of the polynomial 5xy2 + 3x6y4 + 7y9.


Exercise 1

Determine the degree of the following polynomial:

23x4y5 + 17x3yx8 + xy9


Exercise 2

Determine the degree of the following polynomial:

5x10y + 11x2y5 + 3x5y3


Exercise 3

Determine the degree of the following polynomial:

3x20y10 – 6x17y13 – 45x19y11


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