1. Day 1 Lesson Essential Question: How can I use a variety of methods to completely factor expressions and equations?

2. Warm Up Multiply the following binomials. 1) (x+3)(x-2) 2) (x-5)(x-1) 3) (2x+5)(x+1) x 2 +x-6 x 2 -6x+5 2x 2 +7x+5

3. FOIL First Outer Inner Last (x –6)(x –3)

4. FOIL Now YOU try!! First Outer Inner Last (x +2)(x +4)

5. What do these factors help us find?

6. Graph this on your calculator. When a soccer ball is kicked into the air, how long will the ball take to hit the ground? The height h in feet of the ball after t seconds can be modeled by the quadratic function h(t) = –16t 2 + 32t. In this situation, the value of the function represents the height of the soccer ball. When the ball hits the ground, the value of the function is zero.

7. How would you define the zero of a function?

8. Factoring when a=1

9. Factoring Find the zeros of f(x) = x 2 – 6x + 8 by factoring.

10. Methods of Factoring Worksheet

11. Factoring Practice Do #1-3 with a partner on the “Factoring Practice” Worksheet.

12. Check Your Work by Foiling! 1. (x + 9)(x + 2) 2. (y – 7)(y + 5) 3. (g – 6)(g + 2)

13. Difference of Squares When we use it: ◦ Usually in the form ax 2 – c ◦ Both a and c are perfect squares (the square root of each number is a whole number)

14. Difference of Squares Find the zeros of f(x)=h 2 -81 by factoring.

15. Difference of Squares Find the zeros of f(x)=49j 2 -144 by factoring.

16. Methods of Factoring Worksheet

17. Difference of Squares Practice Do #4-10 with a partner on the “Factoring Practice” Worksheet.

18. Factoring (when a ≠ 1):The Welsh Method Steps: 1. Multiply c and a 2. Rewrite the expression with the new value for c 3. Write (ax + )(ax + ) 4. Finish “factoring” the new expression 5. Reduce each set of parentheses by any common factors

19. Factoring (when a ≠ 1):The Welsh Method Find the zeros of f(x) = 3x 2 + 5x - 2 by factoring.

20. Factoring (when a ≠ 1):The Welsh Method Find the zeros of f(x) = 7x 2 - 5x - 2 by factoring.

21. Methods of Factoring Worksheet

22. Factoring (when a ≠ 1):The Welsh Method Do #11-16 with a partner on the “Factoring Practice” Worksheet.

23. GCF (Greatest Common Factor) When we use it: all the terms share 1 or more factors Factoring out GCFs save us time!!! ◦ 4x 2 – 196 = 0 ◦ (2x + 14)(2x – 14) = 0

24. GCF (Greatest Common Factor) Steps: 1. Identify any common factor(s) (including the GCF) 2. Factor out the common factor(s) 3. Factor the remaining expression if possible

25. GCF (Greatest Common Factor) Find the zeros of f(x) = 4x 2 -32x +64 by factoring.

26. GCF (Greatest Common Factor) Find the zeros of f(x)= 3x 4 -24x 3 +21x 2 by factoring.

27. Methods of Factoring Worksheet

28. GCF (Greatest Common Factor) Do #17-27 with a partner on the “Factoring Practice” Worksheet.

29. GCFs and The Welsh Method

30. Methods of Factoring Worksheet

31. GCFs and The Welsh Method Do #28-33 with a partner on the “Factoring Practice” Worksheet.

32. Picking the Right Method -?!?- 34. x 2 + 10x + 16 NOTE: WE HAVE 3 TERMS AND a=1 !!

33. Picking the Right Method -?!?- 35. 5t 2 + 28t + 32 NOTE: WE HAVE 3 TERMS AND a≠1 !!

34. Picking the Right Method -?!?- 16p 2 – 9 NOTE: WE HAVE 2 TERMS WITH A MINUS IN THE MIDDLE AND BOTH TERMS ARE A PERFECT SQUARE !!!!!!!

35. Picking the Right Method -?!?- Do #36-44 with a partner on the “Factoring Practice” Worksheet.

36. Exit Ticket Find the zeros. 1) x 2 -8x-48 2) 4x 2 -49 3) 2x 2 +x-3

37. Warm Up Factor Completely (5 minutes) 1) x 2 -13x+36 2) x 2 -144 3) 6x 2 +13x+6 (x-4)(x-9) (x+12)(x-12) (3x+2)(2x+3)