Polynomials

3 min readJul 17, 2021

A collection of many well defined terms is called polynomial. 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. (5 is the power of x)

P(x)

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 polynomial is defined as the highest degree 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.

There,are three types of polynomial on the basis of there degree:-

Linear Polynomial

Polynomials with 1 as the degree of the polynomial are called linear polynomials. In linear polynomials, the highest exponent of the variable(s) is 1 x + y — 4,
5m + 7n,

Quadratic Polynomial

2p Quadratic polynomial Polynomials with 2 as the degree of the polynomial are called quadratic polynomials. 8x2 + 7y — 9,

Cubic Polynomial

m2 + m — 6 Cubic polynomial Polynomials with 3 as the degree of the polynomial are called cubic polynomials.

Types of Polynomials

Polynomials are of 3 different types and are classified based on the number of terms in it. The three types of polynomials are:

Monomial
Binomial
Trinomial

These polynomials can be combined using addition, subtraction, multiplication, and division but is never division by a variable. A few examples of Non Polynomials are: 1/x+2, x-3

Monomial

A monomial is an expression which contains only one term. For an expression to be a monomial, the single term should be a non-zero term. examples of monomial are:

Binomial

A binomial is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomial. A few examples of binomials are:

– 5x+3,
6a4 + 17x

Trinomials

A trinomial is an expression which is composed of exactly three terms. A few examples of trinomial expressions are:

– 8a4+2x+4

Remainder theorem

If P(x) is divided by (x — a) with remainder r, then P(a) = r.

Factor Theorem

a polynomial f(x) has a factor (x-a), if and only if, f(a) = 0 .

Zero polynomial

If all the coefficients of a polynomial are zero we get a zero degree polynomial.The degree of the zero polynomial is either left undefined, or is defined to be negative .Like any constant value, the value 0 can be considered as a (constant) polynomial, called the zero polynomial.