A polynomial is a mathematical expression consisting of a sum of powers (exponential form) in one or more variables which are multiplied by coefficients. Now we discuss what is polynomial in detail. Polynomial expression are expressions which are combined by the addition, multiplication and subtraction but are not combined by the division. The word polynomial is derived from the Greek word 'poly' which means many. Polynomials are widely used in mathematics and field of science. For instance they are helpful in forming polynomial equation which encodes wide variety of problems, they are also helpful in the field of calculus and other numerical analysis to approximate other Functions.
Monomial, binomial and trinomial are the types of polynomial. Those polynomial which has only one term are known as monomials like 6x, 2x^{4}. Binomial are those polynomials which have two terms in it like y^{2} – y. Those polynomials which have three terms are known as trinomials. For illustration s (y) = y^{2} + y + 4.
A polynomial definition can be a zero and can be written as sum of two or more number of zero. These polynomial terms consist of constant which is coefficient of term which are multiplied by finite number of variables, also called as indeterminants. Each variable has an exponent term which is a natural number, that exponent term is known as degree of that variable, those variables whose degree is not prescribed than we consider it as degree as one. The term which is without variable is the constant term, and the degree of the constant term is zero.
The polynomial with the degree of two are quadratic polynomial and polynomial with degree of three are cubic polynomial and for more than these degrees no specified name is given and they are termed as fourth degree polynomial and fifth degree polynomial.
Any general expression can be a polynomial if expression comprises of constant and variable which is only built up by using addition, subtraction, multiplication. The division of one polynomial by another polynomial does not form polynomial expression. Rational expression is the name given to algebraic fraction where the numerator and denominator are polynomials.
In case of a polynomial involving in one variable, the highest power of the variable is called the degree of the polynomial.
Example: The degree of x^{5} – 2x^{3} + x is 5.
In case of a polynomial involving in more than on...Read More
Types of Polynomials on the basis of number of its terms :
Monomial: A polynomial containing only one non-zero term is called a monomial.
Binomial: A polynomial containing two non-zero terms is called a binomial.
Trin...Read More
Expressions which consist of constants, variables and exponent values joined together by mathematical operators like addition, subtraction, multiplication, are known as polynomials. Exponents can be 0, 1, 2, 3, 4, 5, and 6 ….etc. Polynomials cannot have infinite values. For example: 4xy^{2} – 5x + 5y^{3 }– 8, this given equation is polynomial equation, ...Read More
A polynomial can possess different degrees of variables. Operations like multiplication, addition, subtraction and division with polynomials are same like those with real numbers. Multiplication of polynomials can become complex when done between two polynomials of higher degrees. Only thing we need to remember while multiplying polynomials is: Coefficients o...Read More
Polynomial is an equation which contains various variables and constants. Various operations like polynomial addition and subtraction can be performed. Polynomial division is normally performed with a constant in division of variables. But division by variables is not allowed in formation of polynomials. x^{2} − x/6 + 10 is a polynomial. C...Read More
Exponents can be defined as numbers which represent the number of times a number is multiplied by itself. Let’s understand definition of exponent mathematically. Exponents can be written as numbers above base number. Like 93, this number can also be written as 9 * 9 * 9 = 729. This is what the actual meaning of exponent is.
Now we will focus on polynomials. Poly...Read More