2. FACTORING RULES

3. 2 *GCF( Greatest Common Factor) – First Rule 4 TERMS Grouping 3 TERMS Perfect Square Trinomial AC Method with Grouping 2 TERMS Difference Of Two Squares Sum or Difference Of Two Cubes

4. 3 GCF Greatest Common Factor First Rule to Always Check

5. 4

6. 5

7. 6

8. 7 4 TERMS - Grouping

9. 8

10. 9 3 TERMS 1) Perfect Square Trinomials 2) AC Method With Grouping We will explore factoring trinomials using the ac method with grouping next and come back to Perfect Square Trinomials later.

11. Factoring Trinomials by Using The AC Method With Grouping

12. 11 The first rule of factoring is to factor out the Greatest Common Factor (GCF). Factor the trinomial completely.

13. 12 Stop! Check that you have factored the (GCF) correctly by distributing it back through the remaining polynomial to obtain the original trinomial.

14. 13 To factor, we must find two integers whose product is -60 and whose sum is 7. To factor, we must find two integers whose product is ac and whose sum is b. After factoring out the (GCF), the remaining polynomial is of the form

15. 14 FACTORS OFSUM OF FACTORS OF

16. 15 ac = b = 7 Replace b = 7 in our original expression with b = 12 + (-5).

17. 16 FINISH FACTORING BY GROUPING

18. 17 FACTORED COMPLETELY

19. 18 Practice Problems

20. 19 SUM OF FACTORS OF GCF FACTORS OF KEY #

21. 20 SUM OF FACTORS OF GCF FACTORS OF KEY #

22. 21 SUM OF FACTORS OF GCF FACTORS OF KEY #

23. 22 SUM OF FACTORS OF GCF FACTORS OF KEY #

24. 23 SUM OF FACTORS OF GCF FACTORS OF KEY #

25. 24 SUM OF FACTORS OF GCF FACTORS OF KEY #

26. 25 Answers To Practice Problems

27. 26 Perfect Square Trinomials

28. 27

29. 28 2 TERMS 1) Difference of Two Squares 2) Sum and Difference of Two Cubes

30. 29 Difference of Two Squares

31. 30

32. 31 Sum and Difference of Two Cubes

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36. 35

37. 36 What purpose does factoring serve? Factoring is an algebraic process which allows us to solve quadratic equations pertaining to real-world applications, such as remodeling a kitchen or building a skyscraper. We will cover the concept of solving quadratic equations and then investigate some real- world applications.

38. 37 Solving Quadratic Equations A quadratic equation is an equation that can be written in standard form where a, b, and c represent real numbers, and

39. 38 We will solve some quadratic equations using factoring and the Zero-Factor Property. When the product of two real numbers is 0, at least one of them is 0. If a and b represent real numbers, and if then a=0 or b=0

40. 39 Solve Each Equation

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44. 43 REAL-WORLD APPLICATIONS USING QUADRATIC EQUATIONS

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46. 45

47. 46 The height h in feet reached by a dolphin t seconds after breaking the surface of the water is given by h How long will it take the dolphin to jump out of the water and touch the trainer’s hand?

48. 47 From the top of the building a ball is thrown straight up with an initial velocity of 32 feet per second. The equation below gives the height s of the ball t seconds after thrown. Find the maximum height reached by the ball and the time it takes for the ball to hit the ground.