1 / 46

A quadratic equation is written in the Standard Form ,

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

gareth
Download Presentation

A quadratic equation is written in the Standard Form ,

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. 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 .

  2. 5.8 – Solving Equations by Factoring Zero Factor Property: If a and b are real numbers and if , then or . Examples:

  3. 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).

  4. 5.8 – Solving Equations by Factoring

  5. 5.8 – Solving Equations by Factoring If the Zero Factor Property is not used, then the solutions will be incorrect

  6. 5.8 – Solving Equations by Factoring

  7. 5.8 – Solving Equations by Factoring

  8. 5.8 – Solving Equations by Factoring

  9. 5.8 – Solving Equations by Factoring

  10. 5.8 – Solving Equations by Factoring

  11. 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

  12. 5.8 – Solving Equations by Factoring The square of a number minus twice the number is 63. Find the number. x is the number.

  13. 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

  14. 5.8 – Solving Equations by Factoring Find two consecutive odd numbers whose product is 23 more than their sum? Consecutive odd numbers:

  15. 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

  16. 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).

  17. 6.1 – Rational Expressions – Mult. And Div. What are the values of the variable that make the denominator zero and the expression undefined?

  18. 6.1 – Rational Expressions – Mult. And Div. Simplifying

  19. 6.1 – Rational Expressions – Mult. And Div. Simplifying

  20. 6.1 – Rational Expressions – Mult. And Div. Simplifying

  21. 6.1 - Rational Expressions – Mult. And Div. Multiplication:

  22. 6.1 - Rational Expressions – Mult. And Div. Multiplication:

  23. 6.1 - Rational Expressions – Mult. And Div. Multiplication:

  24. 6.1 - Rational Expressions – Mult. And Div. Division:

  25. 6.1 - Rational Expressions – Mult. And Div. Division:

  26. 6.1 - Rational Expressions – Mult. And Div. Division:

  27. 6.1 - Rational Expressions – Mult. And Div. Division:

  28. 6.2 – Rational Expressions Adding and Subtracting What is the Lowest Common Denominator (LCD)?

  29. 6.2 – Rational Expressions Adding and Subtracting What is the Lowest Common Denominator (LCD)?

  30. 6.2 – Rational Expressions – Add. And Sub. What is the Lowest Common Denominator (LCD)?

  31. 6.2 – Rational Expressions – Add. And Sub. Examples (Like Denominators):

  32. 6.2 – Rational Expressions – Add. And Sub. Examples (Like Denominators):

  33. 6.2 – Rational Expressions – Add. And Sub. Examples (Like Denominators):

  34. 6.2 – Rational Expressions – Add. And Sub. Examples: 15

  35. 6.2 – Rational Expressions – Add. And Sub. Examples: 40x2

  36. 6.2 – Rational Expressions – Add. And Sub. Examples:

  37. 6.2 – Rational Expressions – Add. And Sub. Examples:

  38. 6.2 – Rational Expressions – Add. And Sub. Examples:

  39. 6.2 – Rational Expressions – Add. And Sub. Examples: continued

  40. 6.2 – Rational Expressions – Add. And Sub. Examples:

  41. 6.2 – Rational Expressions – Add. And Sub. Examples: continued

  42. 6.3 – Rational Expressions Simplifying Complex Fractions LCD: 63 Outersover Inners

  43. 6.3 – Rational Expressions Simplifying Complex Fractions LCD: 12, 8 LCD: 24

  44. 6.3 – Rational Expressions Simplifying Complex Fractions LCD: y y–y

  45. 6.3 – Rational Expressions Simplifying Complex Fractions LCD: 6xy 6xy 6xy

  46. END

More Related