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

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

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

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

11. 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 5.8 – Solving Equations by Factoring

12. The square of a number minus twice the number is 63. Find the number. x is the number.

13. 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 5.8 – Solving Equations by Factoring

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

15. 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 5.8 – Solving Equations by Factoring

16. 6.1 – Rational Expressions - A rational expression is a quotient of polynomials. 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). The denominator can not equal zero. Multiplying and Dividing

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

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

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

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

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

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

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

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

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

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

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

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

29. 6.2 – Rational Expressions Adding and Subtracting

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

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

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

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

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

35. Examples: 40x 2 6.2 – Rational Expressions – Add. And Sub.

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

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

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

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

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

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

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

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

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

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

46. END