POLYNOMIALS

 POLYNOMIALS

CONSTANTS

     Constants means a numerical expression which cannot be changed in other words constants are the fixed values. 

Examples of constants are 6, 7, 1.543, 5/7 etc..

VARIABLES

    Variables are represented by an alphabets which can be changed. 

Examples of variables are a, j, m, x etc..

ALGEBRAIC EXPRESSION

     The combination of both variable and constants are called as algebraic expression.

Examples : 4x2-8x+5, 3a2b+5ab2-7

COEFFICIENTS

      Any of the term is multiplied by the variable is called as coefficient of the 

remaining term.

Example: 4x2-8x+5 - In this expression, the variable of x2 is 4 and the variable of x is -8 and 5 is the constant term.

POLYNOMIAL

     A polynomial is an arithmetic expression consisting of variables and constants that involve four arithmetic operations and non-negative integer exponents of variables. 

Generally, polynomials are denoted by f(x), g(x), p(x) and so on.

CONDITIONS OF POLYNOMIALS

     A polynomial exponents contains ONLY WHOLE NUMBERS. It does not contain powers which is negative or fraction.

Example:   6a3-5a+4 - It is polynomial

6a3/5-5a+4 - It is not a polynomial because the expression has power of 'a' is fraction.

6a-3-5a+4   - It is not a polynomial because the exponent of 'a' is negative.

      But  6a3-5a+4,  6a3/5-5a+4,  6a-3-5a+4  these expressions are called as algebraic expression because algebraic expressions of powers or exponents contains whole numbers, fractions and negative. 

STANDARD FORM OF A POLYNOMIAL

      The way of writing the polynomial p(x) in the decreasing or increasing order of the powers of x is called as standard form of polynomial.

Example: 4y2+ 5y4+6y3-y-7 the standard form of this expression is 5y4+6y3+4y2-y-7 or 

-y-7+4y2+6y3+5y4

DEGREE OF THE POLYNOMIAL

      In a polynomial of one variable, the highest power of the variables called the degree of the polynomial.

Example: 5y4+6y3+4y2-y-7 the highest exponent in this

 expression is 4.