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”.
- The meaning of Prefix “Tri” is three.
- 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
$(1) \,\,\,\,\,\,$ $a+b-7$
$(2) \,\,\,\,\,\,$ $x-2y-3$
$(3) \,\,\,\,\,\,$ $-mn^2-mn-0.789$
$(4) \,\,\,\,\,\,$ $\dfrac{1}{2}pqr+pq+6$
$(5) \,\,\,\,\,\,$ $ut+\dfrac{3}{5}t^2-\sqrt{11}$