Polynomial

 

What is a Polynomial?

Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. Examples of constants, variables and exponents are as follows:

• Constants. Example: 1, 2, 3, etc.
• Variables. Example: g, h, x, y, etc.
• Exponents: Example: 5 in x5 etc.

Standard Form of a Polynomial

P(x) = anxn + an-1xn-1 +an-2xn-2 + ………………. + a1x + a0   

Where an, an-1, an-2, ……………………, a1, a0 are called coefficients of xn, xn-1, xn-2, ….., x and constant term respectively and it should belong to real number (⋲ R).

Notation

The polynomial function is denoted by P(x) where x represents the variable. For example,

P(x) = x2-5x+11

If the variable is denoted by a, then the function will be P(a)

Degree of a Polynomial

The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial.