E- LESSON PLAN SUBJECT MATHEMATICS CLASS 8

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(For Teacher)E- LESSON PLA    CLASS 8(maths)
Board - DAV
CLASS –VIII
SUBJECT- MATHEMATICS
CHAPTER 8  :- Polynomials
TOPIC                                                                                       
Chapter:-  8: Polynomials

PRE- REQUISITE KNOWLEDGE:-
All definitions and important terms related to the polynomials of class VI and VII
TEACHING AIDS:- 
Green Board, Chalk,  Duster, Charts, smart board .
METHODOLOGY:- 
Demonstration
OBJECTIVES:-
  • Basic concepts and definitions related to the topic polynomials.
  • Explanation of remainder theorem (long division).
  • Explanation of factor theorem.
  • Method of finding degree and standard form of polynomial.
PROCEDURE :-

Start the session by checking their previous knowledge, by asking the questions related to the topic. After this explain the topic to the students.
S.No
Topic
                       Explanation
1
Introduction, Important Definitions, Degree, standard form .

Polynomial: Polynomials are expressions which are composed of two algebraic terms. It is made up of two terms namely Poly (meaning “many”) and Nominal (meaning “terms.”).  
Example: ax2 +bx + c (Quadratic polynomial).
- An algebraic expression in which the exponent of the variable is a whole number is called  a polynomial.
Types of polynomial  On the basis of terms:-
Monomial:- Polynomial having one term. Eg  4x2
Binomial:-   Polynomial having two terms. Eg   4x2 + 6x
Trinomial:- Polynomial having three terms. Eg   4x2 + 6x + 5
Types of polynomial  On the basis of degree:-
Constant Polynomial:-
A polynomial of degree zero is called constant polynomial 
For Example:-  3, 5
Linear Polynomial:-
Polynomial of degree one is called linear polynomial. 
For Example:- P(x)=  ax + b
Quadratic Polynomial:-
Polynomial of degree two  is called Quadratic polynomial.  
For Example:-  P(x)= ax2 + bx + c
Cubic Polynomial:-
Polynomial of degree three  is called cubic polynomial.   
For Example:- P(x) = ax3 + bx2 + cx + d
Bi-Quadratic Polynomial:-
Polynomial of degree four  is called linear polynomial. 
For Example:- P(x) = ax4 + bx3 + cx2 + dx + e
Zero polynomial:- 
A polynomial with coefficient zero is called zero polynomial
Note:- Degree of zero polynomial is not defined.
Zeroes of polynomial:- 
Values of x for which the given polynomial become zero are called the zeroes of the polynomial.
Note:- Number of zeroes of a polynomial is equal to the degree of that polynomial.
For Example:- A linear polynomial have one zero,  Quadratic polynomial have two zeroes, Cubic polynomial have three zeroes  and so on.
Polynomial Function
A polynomial function is an expression constructed with one or more terms of variables with constant exponents. If there are real numbers denoted by a, then function with one variable and of degree n can be written as:
f(x) = a0xn + a1xn-1 + a2xn-2 + ….. + an-2x2 + an-1x + an
Degree of Polynomials

The degree of polynomials in one variable is the highest power of the variable in the algebraic expression.For a multivariable polynomial, it the highest sum of powers of different variables in any of the terms in the expression.
STANDARD FORM
 A polynomial is in standard form when its term of highest degree is first, its term of 2nd highest is 2nd etc.. Examples of Polynomials inStandard Form. Non-Examples of Polynomials inStandard Form. x2 + x + 3. 2y 4 + 3y 5 + 2+ 7.

Polynomial Division

If a polynomial has more than one term, we use long division method for the same. Following are the steps for it.
  1. Write the polynomial in descending order.
  2. Check the highest power and divide the terms by the same.
  3. Use the answer in step 2 as the division symbol.
  4. Now subtract it and carry down the next term.
  5.  Repeat step 2 to 4 until you have no more terms to carry down.
  6. Note the final answer including remainder in the fraction form (last subtract term).
Division Algorithm:-
            Dividend = Divisor x Quotient + Remainder  or
                    p(x) = g(x) x q(x) + r(x)
2
Types of polynomial on the basis of terms and degrees
3
Divide by factor method
4
Method of division of one polynomial with another and related problems.
5
Method of long division method and problems on it
6
Factorization polynomial
7
Second polynomial is the factor of the first polynomial by division method

                                                                                                                                                                










  EXPECTED OUTCOMES:-
After studying this lesson students will be able  to explain the different types of polynomial. Students should know the method of division of one polynomial with another. Students should be able to factorise the quadratic, cubic and bi-quadratic polynomials.
STUDENTS DELIVERABLES:-
 Review questions given by the teacher. Presentation on the topic factorization and long division method  of polynomials Solve worksheets problems with examples, solve assignment given by the teacher.                  
ASSESSMENT TECHNIQUES:-
Class test , oral test worksheets and assignments .










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