All The Properties In Math And Example For Algebra 1S Classification Of Polynomials Based On Number Of Terms

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Classification Of Polynomials Based On Number Of Terms

Polynomials can be classified based on many different properties. One way to classify polynomials is by counting the number of terms they contain. In this article we will classify polynomials based on the number of terms they contain.

1. Number of terms of a polynomial

Polynomials can be classified according to the number of terms they contain.

Before going 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 ix does not make two terms but one.

In the polynomial 3x + 2, there are two terms, 3x and +2. From the above explanation, the clue is that the terms of polynomials are separated by plus (+) or minus (-) signs.

In the 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.

I hope you are clear about the terms of polynomials. Now we go on to classify polynomials based on the number of terms they contain.

If a polynomial has only one term, it is called a monomial (remember that “mono” means one). Few examples of monomials are 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 called constant polynomials because they contain no variables.

If a polynomial contains two terms, then it is called a binomial (since “bi” means two). Below are some 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 that “tri” means three). Examples of trinomials are shown below;

“a + b + c” is a trinomial because it contains three different terms, a, +bi +c. Similarly, “2m – n + 8” is a trinomial.

If a polynomial contains more than three terms, then it is not used to call by its proper name as in the case of the three previous types, but is called by the general name “polynomial”.

In other words, a polynomial that has 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, we must 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 polynomial with 4 terms. We’ll discuss combining like terms of a polynomial in more depth soon.

So stay tuned as more algebra is on the way.

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