Polynomials1

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Polynomials1

  1. 1. Lets start with a new topic today..
  2. 2. Take this expression 2x2 – 3x + 5 Here 2x2 , 3x, 5 are called as ‘terms’. When we add or subtract terms, it is called a polynomial.
  3. 3. 2x2 – 3√x + 5 Let us check on few expressions… 3y2 – 2y + 4 Is this a polynomial? Yes..it is a proper combo of y terms and number terms Is this a polynomial? No..it is not a polynomial as x is in roots 2x3 – 3 + 4 x Is this a polynomial? No..it is not a polynomial as x becomes x -1 when taken to the numerator.
  4. 4. So, what is not a polynomial? Any polynomial expression with • Roots in the x terms, eg:- 5√x • Negative powers in the x term, eg:- x-2 • x term in the denominator, eg :- 1 x ARE “NOT POLYNOMIALS”
  5. 5. Now let us see whether you are able to figure out whether an expression is a polynomial or not.. Go on to the next page..
  6. 6. Is this a polynomial? 3x – 2
  7. 7. Next one…Is this a polynomial.. 2x2 – 3√x + 5
  8. 8. What about this one? Is it a polynomial.. 1 x2 – 2x + 5
  9. 9. Check this out.. 4x3 + 2x2 – 3x + 1
  10. 10. Let us now check out the degree of a polynomial
  11. 11. Check this expression 4x3 + 2x2 – 3x + 1 Can you see the powers of x ? 4x3 has the power of x as 3 2x2 has the power of x as 2 3x has the power of x as 1 Here The highest power of x is 3. Hence, 3 is the degree of the polynomial
  12. 12. The highest power of x or y or z in a polynomial is called the degree of the polynomial. 4x3 + 2x2 – 3x + 1
  13. 13. Try to figure out the degrees of the polynomial… 3x + 1 2y2 – 2y + 7 5x3 – 3x2 + x – 1 9u3 – 2u4 + u2 – 1 Degree 1 Degree 3 Degree 2 Degree 3 What 3? No..See properly..The highest degree is 4..Just to check whether you are reading smart..
  14. 14. After having seen the degrees of a polynomial, let us see how to classify them according to their degree 3x + 1 Constant Polynomial Linear Polynomial Quadratic Polynomial Cubic Polynomial Eg: - 7 8 3 – x2 4x3 + 2x - 1 If the degree of x is zero or if there is no x term, then it is a constant polynomial If the degree of x is 1, then it is a linear polynomial If the degree of x is 2, then it is a quadratic polynomial If the degree of x is 3, then it is a cubic polynomial
  15. 15. Let us try to figure out the polynomial types according to their degrees….Ready?
  16. 16. Click the correct polynomial type.. 3-x2
  17. 17. Click the correct polynomial type.. 3-x2
  18. 18. Click the correct polynomial type.. 3-x2
  19. 19. Click the correct polynomial type.. 3-x2
  20. 20. Click the correct polynomial type.. 3-x2
  21. 21. Click the correct polynomial type.. √3x2 - 4/3x + ½
  22. 22. Click the correct polynomial type.. 2/3u - 5/2
  23. 23. Click the correct polynomial type.. 9/5x3 – 2x2 + 7/3x – 1/5
  24. 24. Click the correct polynomial type.. 2y3 + 5y – 7
  25. 25. Click the correct polynomial type.. -3/2
  26. 26. Click the correct polynomial type.. 4x – 3
  27. 27. Click the correct polynomial type.. 3y
  28. 28. Click the correct polynomial type.. 4x – 3
  29. 29. Click the correct polynomial type.. 3-x2
  30. 30. 3-x2 √3x2 - 4/3x + ½ 2/3u - 5/2 9/5x3 – 2x2 + 7/3x – 1/5 2y4 + 3 2y3 + 5y – 7 3y 2y2 – 3 4x – 3 -3/2 Quadratic Quadratic Quadratic Linear Linear Linear Cubic Cubic Constant Bi quadratic
  31. 31. Linear polynomial 3x + 2 ax + b Quadratic polynomial 3x2 + 2x + 5 ax2 + bx + c Cubic polynomial 2y3 + 3x2 + 4x + 5 ax3 + bx2 + cx + d
  32. 32. Graph of a polynomial
  33. 33. Y X Y’ X’ ax 2 + bx + c Zeroes of the polynomial Number of zeroes - 2
  34. 34. Find the number of zeroes
  35. 35. Y X Y’ X’
  36. 36. Y X Y’ X’
  37. 37. Y X Y’ X’
  38. 38. Y X Y’ X’
  39. 39. Y X Y’ X’
  40. 40. Y X Y’ X’
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  43. 43. Y X Y’ X’
  44. 44. Y X Y’ X’
  45. 45. Y X Y’ X’
  46. 46. Y X Y’ X’
  47. 47. Y X Y’ X’
  48. 48. Y X Y’ X’
  49. 49. Y X Y’ X’
  50. 50. Y X Y’ X’
  51. 51. Y X Y’ X’
  52. 52. Y X Y’ X’

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