Hiral polynomials mini

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Hiral polynomials mini

  1. 1. K.J. Somaiya Comprehensive College of Education, Training and Research. Name – Hiral Thaker. Std – VIII th. Roll No. – 72. Year 2010 – 2011
  2. 2. What does each prefix mean? <ul><li>mono </li></ul><ul><li>one </li></ul><ul><li>bi </li></ul><ul><li>two </li></ul><ul><li>tri </li></ul><ul><li>three </li></ul><ul><li>poly </li></ul><ul><li>one or more </li></ul>
  3. 3. <ul><li>Polynomial </li></ul>
  4. 4. Objectives The student will be able to: <ul><li>Define polynomial. </li></ul><ul><li>Classify polynomial. </li></ul><ul><li>3. Find the degree of a polynomial. </li></ul>
  5. 5. Polynomial <ul><li>one or more </li></ul><ul><li>A polynomial is a mathematical expression with one or more terms and index of every variable has to be a whole number. </li></ul><ul><li>Eg. 1. 5x 3 </li></ul><ul><li>2. 8y + 7z 2 </li></ul><ul><li>3. m 2 – 3m + 4 </li></ul>
  6. 6. Important Note!! <ul><li>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 . </li></ul><ul><li>Eg. 4x – 7x -2 </li></ul><ul><li>10m + 7m 7/2 </li></ul>
  7. 7. Classification of polynomials <ul><li>Polynomial </li></ul><ul><li>Monomial Binomial Trinomial </li></ul>
  8. 8. Monomial A polynomial of only one term is called a monomial. Eg. -17. 62p. 53a 4 b 3 c.
  9. 9. Binomial <ul><li>A polynomial of two terms is called a binomial. </li></ul><ul><li>Eg. 3p + 9. </li></ul><ul><li>4 – 5a. </li></ul><ul><li>17 – b 3 . </li></ul>
  10. 10. Trinomial <ul><li>A polynomial of three terms is called trinomial. </li></ul><ul><li>Eg. x 2 + 2x + 2. </li></ul><ul><li>a - 9 + 2a 2 . </li></ul><ul><li>13 + n 3 – 6n. </li></ul>
  11. 11. State whether each expression is a polynomial. If it is, identify it. <ul><li>1) 7y - 3x + 4 </li></ul><ul><li>trinomial </li></ul><ul><li>2) 10x 3 yz 2 </li></ul><ul><li>monomial </li></ul><ul><li>3) </li></ul><ul><li>not a polynomial </li></ul>
  12. 12. Which polynomial is represented by <ul><li>x 2 + x + 1 </li></ul><ul><li>x 2 + x + 2 </li></ul><ul><li>x 2 + 2x + 2 </li></ul><ul><li>x 2 + 3x + 2 </li></ul><ul><li>I’ve got no idea! </li></ul>X 2 1 1 X X X
  13. 13. The degree of a monomial is the sum of the exponents of the variables. Find the degree of each monomial. <ul><li>1) 5x 2 </li></ul><ul><li>2 </li></ul><ul><li>4a 4 b 3 c </li></ul><ul><li>8 </li></ul><ul><li>-3 </li></ul><ul><li>0 </li></ul>
  14. 14. To find the degree of a polynomial, find the largest degree of the terms. <ul><li>1) 8x 2 - 2x + 7 </li></ul><ul><li>Degrees: 2 1 0 </li></ul><ul><li>Which is biggest? 2 is the degree! </li></ul><ul><li>2) y 7 + 6y 4 + 3x 4 m 4 </li></ul><ul><li>Degrees: 7 4 8 </li></ul><ul><li>8 is the degree! </li></ul>
  15. 15. Find the degree of x 5 – x 3 y 2 + 4 <ul><li>0 </li></ul><ul><li>2 </li></ul><ul><li>3 </li></ul><ul><li>5 </li></ul><ul><li>10 </li></ul>
  16. 16. Evaluation ??? <ul><li>Q.1)Define polynomial. </li></ul><ul><li>Ans. A polynomial is a mathematical expression with one or more terms and index of every variable has to be a whole number. </li></ul>
  17. 17. <ul><li>Q.2)Are the following expression polynomials ? </li></ul><ul><li>4a 4 + a 3 - 14. </li></ul><ul><li>Ans. Yes, it is a polynomial. </li></ul><ul><li>12 + 10 p -2 </li></ul><ul><li>Ans. No, it is not a polynomial. </li></ul>
  18. 18. Q.3) State the degree of polynomial <ul><li>1) x 3 - 2x + 7 </li></ul><ul><li>Degrees: 3 1 0 </li></ul><ul><li>Which is biggest? 3 is the degree! </li></ul><ul><li>2) 8y 7 + y 4 + x 3 m 4 </li></ul><ul><li>Degrees: 7 4 7 </li></ul><ul><li>7 is the degree! </li></ul>
  19. 19. <ul><li>Thank You !!! </li></ul>

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