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6 .4 – Dividing Polynomials

6 .4 – Dividing Polynomials. Long Division. Review of Long Division. 6.4 – Dividing Polynomials. Long Division. 6.4 – Dividing Polynomials. Long Division. 6.4 – Dividing Polynomials. Long Division. 5.7 - Factoring Polynomials. 20 is the result of the product of 4 and 5.

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6 .4 – Dividing Polynomials

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  1. 6.4 – Dividing Polynomials Long Division Review of Long Division

  2. 6.4 – Dividing Polynomials Long Division

  3. 6.4 – Dividing Polynomials Long Division

  4. 6.4 – Dividing Polynomials Long Division

  5. 5.7 - Factoring Polynomials 20 is the result of the product of 4 and 5. Factoring Trinomials 9 is the result of the sum of 4 and 5. Factors of 20 are:

  6. 5.7 - Factoring Polynomials Factors of 24 are: 1, 24 2, 12 3, 8 4, 6 Factoring Trinomials

  7. 5.7 - Factoring Polynomials Factors of 50 are: 1, 50 2, 25 5,10 Factoring Trinomials

  8. 5.7 - Factoring Polynomials Factors of 9 are: 1, 9 3, 3 Factoring Trinomials

  9. 5.7 - Factoring Polynomials Factors of 12 are: 1, 12 2,6 3, 4 Factors of 2 are: 1, 2 Factoring Trinomials

  10. 5.7 - Factoring Polynomials Factoring Perfect Square Trinomials Not a perfect square

  11. 5.7 - Factoring Polynomials Factoring Perfect Square Trinomials

  12. 5.7 - Factoring Polynomials Factoring the Difference of Two Squares Not the difference

  13. 5.7 - Factoring Polynomials Factoring the Difference of Two Squares

  14. 5.7 - Factoring Polynomials Factoring the Sum or Difference of Two Cubes

  15. 5.7 - Factoring Polynomials Factoring the Sum or Difference of Two Cubes

  16. 5.7 - Factoring Polynomials Factoring the Sum or Difference of Two Cubes

  17. 5.7 - Factoring Polynomials Factoring the Sum or Difference of Two Cubes

  18. 5.8 – Solving Equations by Factoring A quadratic equation is written in the StandardForm, where a, b, and c are real numbers and . Zero Factor Property: If a and b are real numbers and if , then or .

  19. 5.8 – Solving Equations by Factoring Zero Factor Property: If a and b are real numbers and if , then or . Examples:

  20. 5.8 – Solving Equations by Factoring Solving Equations by Factoring: 1) Write the equation to equal zero. 2) Factor the equation completely. 3) Set each factor equal to 0. 4) Solve each equation. 5) Check the solutions (in original equation).

  21. 5.8 – Solving Equations by Factoring

  22. 5.8 – Solving Equations by Factoring If the Zero Factor Property is not used, then the solutions will be incorrect

  23. 5.8 – Solving Equations by Factoring

  24. 5.8 – Solving Equations by Factoring

  25. 5.8 – Solving Equations by Factoring

  26. 5.8 – Solving Equations by Factoring

  27. 5.8 – Solving Equations by Factoring

  28. 5.8 – Solving Equations by Factoring A cliff diver is 64 feet above the surface of the water. The formula for calculating the height (h) of the diver after t seconds is: How long does it take for the diver to hit the surface of the water? seconds

  29. 5.8 – Solving Equations by Factoring The square of a number minus twice the number is 63. Find the number. x is the number.

  30. 5.8 – Solving Equations by Factoring The length of a rectangular garden is 5 feet more than its width. The area of the garden is 176 square feet. What are the length and the width of the garden? The width is w. The length is w+5. feet feet

  31. 5.8 – Solving Equations by Factoring Find two consecutive odd numbers whose product is 23 more than their sum? Consecutive odd numbers:

  32. 5.8 – Solving Equations by Factoring The length of one leg of a right triangle is 7 meters less than the length of the other leg. The length of the hypotenuse is 13 meters. What are the lengths of the legs? meters meters

  33. 6.1 – Rational Expressions - Multiplying and Dividing A rational expression is a quotient of polynomials. The denominator can not equal zero. For any value or values of the variable that make the denominator zero, the rational expression is considered to be undefined at those value(s).

  34. 6.1 – Rational Expressions – Mult. And Div. What are the values of the variable that make the denominator zero and the expression undefined?

  35. 6.1 – Rational Expressions – Mult. And Div. Simplifying

  36. 6.1 – Rational Expressions – Mult. And Div. Simplifying

  37. 6.1 – Rational Expressions – Mult. And Div. Simplifying

  38. 6.1 - Rational Expressions – Mult. And Div. Multiplication:

  39. 6.1 - Rational Expressions – Mult. And Div. 1 Multiplication: 2 1 3

  40. 6.1 - Rational Expressions – Mult. And Div. Multiplication:

  41. 6.1 - Rational Expressions – Mult. And Div. Multiplication:

  42. 6.1 - Rational Expressions – Mult. And Div. Division:

  43. 6.1 - Rational Expressions – Mult. And Div. Division:

  44. 6.1 - Rational Expressions – Mult. And Div. Division:

  45. 6.1 - Rational Expressions – Mult. And Div. Division:

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