Polynomials

Types of Polynomials: Monomial, Binomial, Trinomial

Polynomials are algebraic expressions that may comprise of exponents which are added, subtracted or multiplied. Polynomials are of different types. Namely, Monomial, Binomial, and Trinomial. 

A monomial is a polynomial with one term. 

A binomial is a polynomial with two, unlike terms. 

A trinomial is an algebraic expression with three, unlike terms.

In simple words, polynomials are expressions comprising a sum of terms, where each term holding a variable or variables is elevated to power and further multiplied by a coefficient. Amusingly, the simplest polynomials hold one variable.

Types of Polynomials

1. Monomials – Monomials are the algebraic expressions with one term, hence the name “Mono”mial. In other words, it is an expression that contains any count of like terms. For example, 2x + 5x + 10x is a monomial because when we add the like terms it results in 17x. Furthermore, 4t, 21x2y, 9pq etc are monomials because each of these expressions contains only one term.
2. Binomials – Binomials are the algebraic expressions with two unlike terms, hence the name “Bi”nomial. For example, 3x + 4x2 is binomial since it contains two unlike terms, that is, 3x and 4x2. Likewise, 10pq + 13p2q is a binomial.
3. Trinomials – Trinomials are the algebraic expressions with three unlike terms, hence the name “Tri”nomial. For example- 3x + 5x2 – 6x3 is a trinomial. It is due to the presence of three, unlike terms, namely, 3x, 5x2 and 6x3. Likewise, 12pq + 4x2 – 10 is a trinomial.

There is another type of polynomial called the zero polynomial. In this type, the value of every coefficient is zero. For example: 0x2 + 0x – 0

Degree of a Polynomial

It is simply the greatest of the exponents or powers over the various terms present in the algebraic expression.

NB:- Rene Descartes invented polynomials. He is one of those who were responsible for introducing the concept of the graph of polynomial equations in 1637 in La geometric.