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Classification Of Polynomials Based On Number Of Terms
Polynomials can be classified according to many different properties. One way to classify polynomials is to count the number of terms they contain. In this article, we will classify polynomials according to the number of terms they contain.
1. Number of terms in a polynomial
Polynomials can be classified according to the number of terms they contain.
Before moving on to explain the classification of polynomials based on the number of terms; First I want to explain the number of terms in a polynomial.
In the simplest polynomial, “3x”, there is only one term. Note that 3 and x are not two terms but one.
In the polynomial 3x + 2, there are two terms, 3x and +2. From the explanation above, the clue is that the terms of the polynomials are separated by plus (+) or minus (-) signs.
In the polynomial “x + 2xy – 3y – 12”, there are four terms, x, +2xy, – 3y and -12. Notice that I write the signs with the terms, because signs are always important in math.
I hope you are clear on the terms of the polynomials. Now let’s move on to the classification of polynomials according to the number of terms they contain.
If a polynomial has only one term, it is called a monomial (remember; “mono” means one). There are few examples of monomials given below;
“9a”, “-9a” or “2xy” or “-5abc” are all examples of monomials. Numbers, such as 1, -1, 2, -2, etc., are also monomials, but they are instead called constant polynomials because they do not contain any variables.
If a polynomial contains two terms, then it is called a binomial (because “bi” means two). Here are some examples of binomials;
“2m + 2”, “-3a + b” or “3xy – 2abc”, are all binomials.
If a polynomial contains three terms, it is called a trinomial (remember; “tri” means three). Here are examples of trinomials;
“a + b + c” is a trinomial because it contains three different terms, a, +b and +c. Similarly, “2m – n + 8” is a trinomial.
If a polynomial contains more than three terms, it is not used to call by its proper name as in the case of the three types above, but is called by the 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 like terms in a polynomial, then we have to combine the like terms of that polynomial before naming it. For example;
“2x + 3x – 3b + 5” contains three terms instead of four.
There are two like terms in the polynomial, which are “2x” and “3x” (like terms contain the same variables) and we count them as one term. So “2x + 3x – 3b + 5” is a trinomial, not a 4-term polynomial. We will soon discuss in more detail the combination of similar terms of a polynomial.
So stay tuned because more algebra is on the way.
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