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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 .

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14 March 2011

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  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

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