Polynomials
An algebraic expression that contains one or more terms is called a polynomial.
Introduction
The meaning of polynomial is defined from a prefix “Poly” and a Latin term “Nomial”.
- The meaning of prefix “Poly” is many.
- The meaning of “Nomial” is a term.
The meaning of a polynomial is an algebraic expression with one or more terms according to the meanings of poly and nomial. A polynomial actually represents a quantity by one or more terms in mathematical form.
In a polynomial, one term or two or more unlike terms are connected by either plus or minus or both signs for expressing a quantity in algebraic form in mathematics. Polynomials are formed in mathematical form in two different ways.
A polynomial is a monomial, binomial, trinomial, quadrinomial and all multinomials.
One or More term
A polynomial is purely formed by one term or two or more unlike algebraic terms.
Examples
$(1) \,\,\,\,\,\,$ $-7a$
$(2) \,\,\,\,\,\,$ $c^2+0.18d^3$
$(3) \,\,\,\,\,\,$ $ap-q^2+\sqrt{5}r$
$(4) \,\,\,\,\,\,$ $m-7mn+9n^2-10n$
$(5) \,\,\,\,\,\,$ $8x$ $+$ $xy$ $-$ $5y^2$ $-$ $yz$ $+$ $z^5$
A number with terms
A polynomial is also formed by a number and one or more algebraic terms.
Examples
$(1) \,\,\,\,\,\,$ $11$
$(2) \,\,\,\,\,\,$ $a-3$
$(3) \,\,\,\,\,\,$ $8d+ef+\dfrac{1}{3}$
$(4) \,\,\,\,\,\,$ $p+pq+4pq^2+23$
$(5) \,\,\,\,\,\,$ $x-2y-x^2y^2+7xy^2+\sqrt[8]{17}$