Polynomial Definition

In Mathematics, a polynomial is defined as an algebraic expression which consists of variables, coefficients, and mathematical operations such as addition, subtraction, multiplication or division. In this article, let us discuss the polynomial definition, its standard form, types, examples and applications.

Polynomial Definition in Maths

A polynomial is defined as an expression which consists of single or multiple terms. The term polynomial is originated from two different terms such as “poly” and “Nomial”. The term “poly” means many and “nomial” means terms. In short, a polynomial is an algebraic expression which has two or more algebraic terms. It has variables, constants, coefficients, exponents and operators. In case, if an expression has negative number expressions, it is not considered as a polynomial.

Variable: An alphabet which is used to represent the unknown value

Coefficient: A number which is multiplied with the variable

Operator: Operator may be either addition (+), subtraction (-), multiplication (*), etc.

Constant: The value which cannot be changed is called constant

Standard Form of a Polynomial

The general form to represent the polynomial is as follows:

\(F(x)= a_{n}x^{n} + a_{n-1}x^{n-1} + a_{n-2}x^{n-2} + …+a_{1}x+a_{0}\)

Here, a0 ,….an is a constant

x is a variable

Types of Polynomial

The different types of polynomial expressions are:

  • Monomial – Expression with a single term. Example 4x
  • Binomial – Expression with two terms. Example: 4x+5y
  • Trinomial – Expression with exactly three terms. Example: 7x2 + 5y – 2z

Applications of Polynomials

The applications of polynomials are given below:

  • Polynomials are used in physics, chemistry, and electronics
  • It is used in construction
  • Used in Roller coaster design to describe the curves
  • Mathematical models are used in meteorology, to represent weather patterns.

Polynomials Example

Question:

Determine if the given expression is polynomial or not.

  1. 6x2 (b) 7x+8y (c) 4x-3

Solution:

(a) 6x2 – The given term is a polynomial with a single term (monomial)

(b) 7x+8y – It is a polynomial with two terms (Binomial)

(c) 4x-3 – The given term is not a polynomial because it has negative exponents.(i.e) -3

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