Math CentralQuandaries & Queries


Question from Nichole, a student:

How do I determine the degree of polynomials? I've searched this on sites but they are
all so confusing! Is there a simple explanation or way to find what the degree is? Some
examples are: 6x^4 10x^2yz^5 and 3m^2n^7-10m^8. I also have to say that I am
under the impression that this symbol ^ means the number after it is an exponent.

You are correct about the meaning of ^. x^2 and x² mean the same.

The degree of a term (product of variables and their powers) is the sum of its exponents (including "1" for any variable without an explicit exponent.) Constants have no effect. So the terms $x^5, 7x^4y$, and $(1/2)xy^3z$ all have degree 5. A constant term has degree 0.

The degree of a polynomial is the degree of its highest-degree term. So $x^4 + 2wxy^2z$ has degree 5.

Good Hunting!


You need o be sure to simplify an expression before determining its degree. For example the polynomial $4x^3 + 5x^2 - 3x^3 + 7 - x^3$ has degree 2 since simplified is is $5x^2 + 7.$


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