   SEARCH HOME Math Central Quandaries & 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!
RD

Nichole,

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 $5x^2 + 7.$

Harley      Math Central is supported by the University of Regina and the Imperial Oil Foundation.