This document discusses different types of polynomials. It defines a polynomial as an algebraic expression with variable powers that are whole numbers. It then describes polynomials according to their degree as linear, quadratic or cubic. It also categorizes polynomials according to their terms as monomials, binomials or trinomials. Specific examples are provided for each type of polynomial. The document also contains solutions to problems determining whether certain algebraic expressions are polynomials or not.

1. MATHEMATICS
STD-IX
MATHEMATICS
STD-IX

2. Chapter 8

3. Polynomial
An algebraic expression in which all variable have
power as a whole number is called polynomial.
For example: x²+3x+6
Maximum power of variable of polynomial.
Eg: 4x⁵+5x²+2x+1.

4.  According to Degree
1) Linear
2) Quadratic
3) Cubic
 According to Terms
1) Monomial
2) Binomial
3) Trinomial

5. 1. Linear polynomial:
The polynomials have degree 1.
Eg: 2x+5.
2. Quadratic Polynomial:
The polynomial has degree 2.
Eg: 4x²+8x+5.
3. Cubic polynomial:
The polynomial has degree of 3.
Eg: x³+4x+5.

6. 1.Monomial:
A polynomial has only one term.
Eg: 2x.
2. Binomial:
A polynomial has two terms.
Eg: 2x+7y.
3.Trinomial:
A polynomials has three terms.
Eg: x²+3x+5.

8. solution:
Q1: Length of the ground = x
Length of the ground including the path = x+1+1 =x+2
Area of the ground including the path =(x+2)² =x²+4x+4
Area of the ground =x²
‫؞‬ Area of path = x²+4x+4-x²
=4x+4 x+2
4x+4 is a polynomial.
x+2
1 1
1 1

9. Solution:
Q2: Number be = x
Reciprocal of the number =1∕x
‫؞‬Sum = x+ 1∕x
x+ 1∕x is not a polynomial.

10. Homework:
Find out following are polynomial?
1. Sum of a number and its square root.
1. Product of the sum and the difference of a
number and its square root.

11. JINSHA K