1 / 55

14 March 2011

14 March 2011. Algebra 2. Composition of Functions. (3x – 1)*(x 2 + 3x – 4). Multiplying a Binomial and Trinomial . Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials. Composition of Functions. (3x – 1)*(x 2 + 3x – 4) 3x 3. Multiplying a Binomial and Trinomial .

Download Presentation

14 March 2011

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 14 March 2011 Algebra 2

  2. Composition of Functions (3x – 1)*(x2 + 3x – 4) Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  3. Composition of Functions (3x – 1)*(x2 + 3x – 4) 3x3 Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  4. Composition of Functions (3x – 1)*(x2 + 3x – 4) 3x3 + 9x2 Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  5. Composition of Functions (3x – 1)*(x2 + 3x – 4) 3x3 + 9x2 – 12x Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  6. Composition of Functions (3x – 1)*(x2 + 3x – 4) 3x3 + 9x2 – 12x – x2 Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  7. Composition of Functions (3x – 1)*(x2 + 3x – 4) 3x3 + 9x2 – 12x – x2– 3x Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  8. Composition of Functions (3x – 1)*(x2 + 3x – 4) 3x3 + 9x2 – 12x – x2– 3x + 4 Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  9. Composition of Functions (3x – 1)*(x2 + 3x – 4) 3x3 + 9x2 – 12x – x2 – 3x + 4 Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  10. Composition of Functions (3x – 1)*(x2 + 3x – 4) 3x3 + 9x2 – 12x – x2 – 3x + 4 Multiplying a Binomial and Trinomial Combine like terms Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  11. Composition of Functions (3x – 1)*(x2 + 3x – 4) 3x3 + 9x2– 12x – x2– 3x + 4 Multiplying a Binomial and Trinomial Combine like terms Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  12. Composition of Functions (3x – 1)*(x2 + 3x – 4) 3x3 + 9x2– 12x – x2– 3x + 4 3x3 + 8x2 – 15x + 4 Multiplying a Binomial and Trinomial Final answer Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  13. Multiply (x - 3)(2x2 + 3x – 5) • 2x3 – 3x2 – 14x + 15 • 3x3 – 3x2 – 14x – 15 • 2x3 – 6x2 – 9x + 15 • 3x3 – 6x2 – 14x – 15 • 2x3 + 3x2 + 14x - 15 0 of 30

  14. Composition of Functions (2x – 3)3 = ? Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  15. Composition of Functions (2x – 3)3 = (2x – 3)(2x – 3)(2x – 3) Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  16. Composition of Functions (2x – 3)3 = (2x – 3)(2x – 3)(2x – 3) Multiply these two using FOIL or Box method Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  17. Composition of Functions (2x – 3)3 = (2x – 3)(2x – 3)(2x – 3) Multiply these two using FOIL or Box method: 2x - 3 2x -3 Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  18. Composition of Functions (2x – 3)3 = (2x – 3)(2x – 3)(2x – 3) Multiply these two using FOIL or Box method: 2x - 3 2x 4x2 -6x -3 -6x +9 Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  19. Composition of Functions (2x – 3)3 = (2x – 3)(2x – 3)(2x – 3) Multiply these two using FOIL or Box method: 2x - 3 2x 4x2 -6x -3 -6x +9 4x2 – 12x + 9 Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  20. Composition of Functions (2x – 3)3 = (2x – 3)(2x – 3)(2x – 3) = (2x – 3)(4x2 – 12x + 9) Substitute the trinomial we just found Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  21. Composition of Functions (2x – 3)3 = (2x – 3)(2x – 3)(2x – 3) = (2x – 3)(4x2 – 12x + 9) 8x3– 24x2+ 18x Multiply Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  22. Composition of Functions (2x – 3)3 = (2x – 3)(2x – 3)(2x – 3) = (2x – 3)(4x2 – 12x + 9) 8x3 – 24x2 + 18x – 12x2+ 36x – 27 Multiply Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  23. Composition of Functions (2x – 3)3 = (2x – 3)(2x – 3)(2x – 3) = (2x – 3)(4x2 – 12x + 9) 8x3 – 24x2 + 18x – 12x2 + 36x – 27 Combine like terms Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  24. Composition of Functions (2x – 3)3 = (2x – 3)(2x – 3)(2x – 3) = (2x – 3)(4x2 – 12x + 9) 8x3– 24x2+ 18x – 12x2+ 36x – 27 8x3 – 36x2 + 54x – 27 Final answer Multiplying a Binomial and Trinomial Mathematics.XEI.504: (24-27) Add, subtract, and multiply polynomials

  25. Multiplying Polynomials • Complete questions 51- 60 • Write the question number on your work-sheet • Show your work on your work-sheet • Write the answer letter on your work-sheet • You have 15 minutes

  26. Factoring Polynomials 5x + 5y + 5z = ? Factoring a common term Mathematics.XEI.505: (24-27) Factor simple quadratics

  27. Factoring Polynomials 5x + 5y + 5z = ? Look for something that is the same in each term Factoring a common term Mathematics.XEI.505: (24-27) Factor simple quadratics

  28. Factoring Polynomials 5x + 5y + 5z = ? Look for something that is the same in each term Factoring a common term Mathematics.XEI.505: (24-27) Factor simple quadratics

  29. Factoring Polynomials 5x + 5y + 5z = ? 5(x + y + z) Write that outside a set of parentheses, and write what is left inside Factoring a common term Mathematics.XEI.505: (24-27) Factor simple quadratics

  30. Factoring Polynomials 4x2 + 5xy + 6xz = ? Look for something that is the same in each term Factoring a common term Mathematics.XEI.505: (24-27) Factor simple quadratics

  31. Factoring Polynomials 4x2 + 5xy + 6xz = ? Look for something that is the same in each term Factoring a common term Mathematics.XEI.505: (24-27) Factor simple quadratics

  32. Factoring Polynomials 4x2 + 5xy + 6xz = ? x(4x + 5y + 6z) Write that outside a set of parentheses, and write what is left inside Factoring a common term Mathematics.XEI.505: (24-27) Factor simple quadratics

  33. opq + opr + ops = ? • o(pq + pr + ps) • p(oq + or + os) • pq(o + r + s) • op(q + r + s) 0 of 30

  34. Factoring Polynomials If there are only two terms given to you, you probably have a difference of squares. Difference of Squares Mathematics.XEI.505: (24-27) Factor simple quadratics

  35. Factoring Polynomials If there are only two terms given to you, you probably have a difference of squares. Example: x2 – 25 Difference of Squares Mathematics.XEI.505: (24-27) Factor simple quadratics

  36. Factoring Polynomials Example: x2 – 25 Difference of Squares Mathematics.XEI.505: (24-27) Factor simple quadratics

  37. Factoring Polynomials Example: x2 – 25 Solution: ( )( ) Difference of Squares Mathematics.XEI.505: (24-27) Factor simple quadratics

  38. Factoring Polynomials Example: x2 – 25 Solution: ( )( ) Difference of Squares Mathematics.XEI.505: (24-27) Factor simple quadratics

  39. Factoring Polynomials Example: x2 – 25 Solution: (x )(x ) Difference of Squares Mathematics.XEI.505: (24-27) Factor simple quadratics

  40. Factoring Polynomials Example: x2 – 25 Solution: (x )(x ) Difference of Squares Mathematics.XEI.505: (24-27) Factor simple quadratics

  41. Factoring Polynomials Example: x2 – 25 Solution: (x 5)(x 5) Difference of Squares Mathematics.XEI.505: (24-27) Factor simple quadratics

  42. Factoring Polynomials Example: x2 – 25 Make one ‘+’ and one ‘-’ Solution: (x 5)(x 5) Difference of Squares Mathematics.XEI.505: (24-27) Factor simple quadratics

  43. Factoring Polynomials Example: x2 – 25 Make one ‘+’ and one ‘-’ Solution: (x + 5)(x - 5) Difference of Squares Mathematics.XEI.505: (24-27) Factor simple quadratics

  44. Factoring Polynomials Example: x2 – 25 Solution: (x + 5)(x - 5) Difference of Squares Mathematics.XEI.505: (24-27) Factor simple quadratics

  45. Factoring Polynomials • Complete questions 61- 70 • Write the question number on your work-sheet • Show your work on your work-sheet • Write the answer letter on your work-sheet • You have 10 minutes

  46. Factoring Polynomials -Identify a,b,c x2 + 4x - 12= 0 Factor a Quadratic Mathematics.XEI.503

  47. Factoring Polynomials -Identify a,b,c x2 + 4x - 12= 0 a b c Factor a Quadratic Mathematics.XEI.503

  48. Factoring Polynomials -Identify a,b,c x2 + 4x - 12= 0 a b c a = 1 b = 4 c = -12 Factor a Quadratic Mathematics.XEI.503

  49. Factoring Polynomials -Multiply a and c x2 + 4x - 12= 0 a = 1 c = -12 ac = -12 Factor a Quadratic Mathematics.XEI.503

  50. Factoring Polynomials -Make a chart listing the factors of ac ac = -12 b = 4 Factor a Quadratic Mathematics.XEI.503

More Related