# Trinomials

An algebraic expression that contains three terms is called a trinomial.

## Introduction

The meaning of trinomial is defined from a prefix “Tri” and a Latin term “Nomial”.

1. The meaning of Prefix “Tri” is three.
2. The meaning of “Nomial” is a term.

On the basis of the meanings of both terms, the term trinomial is defined in algebra as an algebraic expression with three terms. A trinomial is usually formed by three unlike terms to represent a quantity in mathematical form.

In a trinomial, the three unlike terms are connected by plus or minus or both to form an algebraic expression. In algebra, a trinomial is also called as a polynomial of three terms and it is possibly formed in two different forms.

### Three Unlike Algebraic Terms

The trinomials are also formed purely by three unlike algebraic terms in some cases.

##### Examples

$(1) \,\,\,\,\,\,$ $a+b+c$

$(2) \,\,\,\,\,\,$ $x-y+z$

$(3) \,\,\,\,\,\,$ $pq+qr+rs$

$(4) \,\,\,\,\,\,$ $-mn-2m^2n^2-3m^3n^3$

$(5) \,\,\,\,\,\,$ $u-\dfrac{3}{7}u^2-\sqrt[4]{8}u^3$

### Two terms and a Number

The trinomials are also formed by three unlike terms but two terms are unlike algebraic terms and other term is a number.

##### Examples

$(1) \,\,\,\,\,\,$ $a+b-7$

$(2) \,\,\,\,\,\,$ $x-2y-3$

$(3) \,\,\,\,\,\,$ $-mn^2-mn-0.789$

$(4) \,\,\,\,\,\,$ $\dfrac{1}{2}pqr+pq+6$

$(5) \,\,\,\,\,\,$ $ut+\dfrac{3}{5}t^2-\sqrt{11}$

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