Question

Explain me what is polynomials for class 9 ? With 5 Solved Examples?

Answer 1

A Polynomial can be expressed in terms that only have positive integer exponents and the operations of addition, subtraction, and multiplication. In other words, it must be possible to write the expression without division. It's easiest to understand what makes something a polynomial equation by looking at examples and non examples as shown below.

Examples of Polynomials

Example Polynomial Explanation
x2 + 2x +5 Since all of the variables have integer exponents that are positive this is a polynomial.
5x +1 Since all of the variables have integer exponents that are positive this is a polynomial.
(x7 + 2x4 - 5) * 3x Since all of the variables have integer exponents that are positive this is a polynomial.
5x-2 +1 Not a polynomial because a term has a negative exponent
3x½ +2 Not a polynomial because a term has a fraction exponent
(5x +1) ÷ (3x) Not a polynomial because of the division
(6x2 +3x) ÷ (3x) Is actually a polynomial because it's possible to simplify this to 3x + 1 --which of course satisfies the requirements of a polynomial. (Remember the definition states that the expression 'can' be expressed using addition,subtraction, multiplication. So, if it's possible to simplify an expression into a form that uses only those operations and whose exponents are all positive integers...then you do indeed have a polynomial equation)
Polynomial Equation- is simply a polynomial that has been set equal to zero in an equation.

Answer 2

Hiii friend,


Before understanding the polynomial First we will have to understand constant and variable.

Constant :- A symbol having a fixed numerical Value is called a constant.

Examples:- 8 , -6 , 5/7 all are constant.


Variable:- A symbol which may be assigned different numerical values is know as a variable.

Examples :- X , Y , Z , All are variable.

POLYNOMIAL:-

AN algebraic expression in which the variables involved have only non-negative integral powres is called a polynomial.

Examples:- (1) 5X³-4X²+6X-2 is a POLYNOMIAL in one variable where variable is X.

(2) 9Y⁴+6Y³+10Y²-8Y+2/5 is also a polynomial in one variable Y.

(3) 3+2X²-6X²Y+5XY² is a polynomial in two variables X and Y.

(4) 3X²+Y²+45 is a polynomial in two variables X and Y.


HOPE IT WILL HELP YOU...... :-)