Monday, November 28, 2011

Degree of a Polynomial

One of the most common questions you will find when first learning about polynomials, "How do you find the degree of a polynomial," sounds incredibly complicated and difficult, but really couldn't be simpler.  Sometimes, you don't need to use a bunch of math concepts to find the answer, or to do several mathematical manipulations to arrive at the solution.  Often, you don't have to do anything but just LOOK at the equation, and you can figure out the degree of a polynomial.  And that is because finding the degree of a polynomial is simple.

The degree of a polynomial is simply the highest exponent of the variable in the equation.

Look at this question, and you will see just how easy it can be:

What is the degree of the polynomial:  x3 + x = 5.

Yes, it is as simple as it sounds.  The highest power of x in this polynomial is 3, and so that is the degree.  See? Told you it can be easy!

Your questions will likely look similar to that one.  However, there are a few things to say as well, just in case you get a curve ball question.

Non-zero terms (e.g. integers) have a variable with an exponent of 0 (which means that the variable actually equals 1, and therefore you don't need to show it).  If you ONLY have non-zero integer, and therefore assume you have a variable with an exponent of 0, you can say that the degree of this non-zero constant polynomial is 0.  That is, constants are zero-degree.  However, that is only for non-zero polynomials.  Zero itself has an undefined degree.

So, the degree of the non-zero constant polynomial 8 is 0.  Easy.

Of course, you will inevitably get harder questions that do actually require a bit of work to arrive at your solution, but that will only be more of the same kind of mathematical concepts you've been studying, such as how to FOIL polynomials, or factoring by grouping.  In the end, when you have your polynomial expression, all you need to do is determine what is the highest exponent of the variable, and then state that as the degree.  Try some practice questions, and you will find that you won't be asking "how do you find the degree of a polynomial" anymore!

One last thought I'd like you to consider:  I have seen people searching my site for help with things like "degree polynomial" or "degree polynomials" and I think that sounds very strange, and suggests to me that this math concept is not being taught very well at all in the classroom.  Technically, you don't have "degree polynomials" per se.  ALL polynomials, except zero, have a degree which can be anything from third degree polynomials to higher degree polynomials such as ten-thousand degree polynomials (though I certainly don't want to be the one working with a polynomial of that degree!).  If you think about it, to say something like a "degree polynomial" is to be redundant!

In any case, if you arrived here after searching for help with finding the degree of a polynomial, or for "degree polynomial," I hope this post has been informative and helpful for you.  It's not a math concept that is as hard as it sounds, so hopefully my post makes sense and you can take something away to help teach other students who don't know what "degree polynomials" are.  :-)  As always, please remember to +1 me below if you liked my post!  Also follow me on Twitter with the button above!

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