Classification Of Polynomials Based On Number Of Terms

Polynomials can be classified based on many different properties. One way to classify the polynomials is by counting number of terms they contain. In this article we will classify the polynomials based on number of terms in them.
1. Number of terms in a polynomial Polynomials can be classified based on the number of terms they contain. Before I move to explain the classification of polynomials based on number of terms; I want to explain the number of terms in a polynomial, first.

In simplest polynomial, "3x", there is only one terms. Note that, 3 and x don't make two terms but one. In polynomial 3x + 2, there are two terms, 3x and +2. From above explanation, the hint is that, the terms of polynomials are separated by plus (+) or minus signs (-).
In polynomial "x + 2xy - 3y - 12", there are four terms, x, +2xy, - 3y and -12.
Note that, I am writing the signs with the terms, as signs are always important in mathematics.
Hope that you are clear about the terms of polynomials.

Now let's move on to classify the polynomials on the basis of the number of terms they contain.

If a polynomial has one term only, it is called a monomial (remember; "mono" means one).
There are few examples of monomials given below; "9a", "- 9a" or "2xy" or "-5abc" all are the examples of monomials. Numbers, such as, 1, -1, 2, -2 and so on, are also monomials, but they are called constant polynomials instead because they contain no variables. If a polynomial contain two terms, then it is called a binomial (as "bi" means two). Following are some of the examples of binomials; "2m + 2", "-3a + b" or "3xy - 2abc", are all binomials. If a polynomial contains three terms, then it is called a trinomial (remember; "tri" means three). Following are the examples of trinomials; "a + b + c" is a trinomial, as it contain three different terms, a, +b and +c.
Similarly, "2m - n + 8" is a trinomial. If a polynomial contain more than three terms, then it is not used to call by its proper name as in case of above three types, but is called by general name "polynomial" instead.
In other words a polynomial having four or more terms is called a "polynomial".

What if there are two or more similar terms in a polynomial? If there are two or more similar terms in a polynomial, then we have to combine the like terms of that polynomial before we name it.
For example; "2x + 3x - 3b + 5" contains three terms, instead of four.
There are two similar terms in the polynomial, which are "2x" and "3x" (similar terms contain the same variables) and we count them as one term. Hence, "2x + 3x - 3b + 5" is a trinomial, not a polynomial with 4 terms.

We will discuss the combining the like terms of a polynomials in more depth soon.
So, stay tuned as more algebra is on its way.