- This document defines key terms related to polynomials such as mono, bi, tri, and poly prefixes and defines a polynomial as a mathematical expression with one or more terms where the variable index is a whole number. - Polynomials are classified as monomials (one term), binomials (two terms), or trinomials (three terms). Degrees of polynomials and monomials are defined as the sum of the exponents of the variables. - Examples are provided to demonstrate identifying polynomials and classifying them by type, as well as finding the degree of monomials and polynomials.

1. K.J. Somaiya Comprehensive College of Education, Training and Research. Name – Hiral Thaker. Std – VIII th. Roll No. – 72. Year 2010 – 2011

2. What does each prefix mean? mono one bi two tri three poly one or more

3. Polynomial

4. Objectives The student will be able to: Define polynomial. Classify polynomial. 3. Find the degree of a polynomial.

5. Polynomial one or more A polynomial is a mathematical expression with one or more terms and index of every variable has to be a whole number. Eg. 1. 5x 3 2. 8y + 7z 2 3. m 2 – 3m + 4

6. Important Note!! An expression is not a polynomial if there is a variable in the denominator or the index of the variable is negative or a fraction . Eg. 4x – 7x -2 10m + 7m 7/2

7. Classification of polynomials Polynomial Monomial Binomial Trinomial

8. Monomial A polynomial of only one term is called a monomial. Eg. -17. 62p. 53a 4 b 3 c.

9. Binomial A polynomial of two terms is called a binomial. Eg. 3p + 9. 4 – 5a. 17 – b 3 .

10. Trinomial A polynomial of three terms is called trinomial. Eg. x 2 + 2x + 2. a - 9 + 2a 2 . 13 + n 3 – 6n.

11. State whether each expression is a polynomial. If it is, identify it. 1) 7y - 3x + 4 trinomial 2) 10x 3 yz 2 monomial 3) not a polynomial

12. Which polynomial is represented by x 2 + x + 1 x 2 + x + 2 x 2 + 2x + 2 x 2 + 3x + 2 I’ve got no idea! X 2 1 1 X X X

13. The degree of a monomial is the sum of the exponents of the variables. Find the degree of each monomial. 1) 5x 2 2 4a 4 b 3 c 8 -3 0

14. To find the degree of a polynomial, find the largest degree of the terms. 1) 8x 2 - 2x + 7 Degrees: 2 1 0 Which is biggest? 2 is the degree! 2) y 7 + 6y 4 + 3x 4 m 4 Degrees: 7 4 8 8 is the degree!

15. Find the degree of x 5 – x 3 y 2 + 4 0 2 3 5 10

16. Evaluation ??? Q.1)Define polynomial. Ans. A polynomial is a mathematical expression with one or more terms and index of every variable has to be a whole number.

17. Q.2)Are the following expression polynomials ? 4a 4 + a 3 - 14. Ans. Yes, it is a polynomial. 12 + 10 p -2 Ans. No, it is not a polynomial.

18. Q.3) State the degree of polynomial 1) x 3 - 2x + 7 Degrees: 3 1 0 Which is biggest? 3 is the degree! 2) 8y 7 + y 4 + x 3 m 4 Degrees: 7 4 7 7 is the degree!

19. Thank You !!!