1. Factor the following. 1) 20x 2 - 115x – 302) x 2 + 4x – 96 3)14a 2 b - 63a 5 b 6 4)12x 3 +3x 2 +20x +5

2. September 4 th

3. Multiply (x – 2) (x + 2)…. This product is a little different than the rest. What is it missing? A middle term!

4. If given x 2 – 4, and asked to factor, how could you set this up using what you know already? What is the middle coefficient, b ? What is the last number, c ? Can you find two numbers that add to be zero and multiply to be – 4 ? -4 0

5. a 2 - b 2 = (a - b) (a + b) x 2 - 2 2 = (x - 2) (x + 2) x 2 – 4 = (x - 2) (x + 2) This only works for the DIFFERENCE, not sum/addition!

6. Factor x 2 - 9 = (a - b) (a + b) What number squared is 9? So… (x - 3) (x + 3) Check your answer by FOIL or box!

7. What if there is a coefficient in the front? 4x 2 – 25 It works the same way! What number squared is 4? 25? (2x - 5) (2x + 5)

8. 1) x 2 – 144 2) w 2 – 64 3) 16m 2 – 49 4) x 2 + 25

9. Multiply (x + 6) (x + 6)…. What do you notice about the product? Can you find a pattern?

10. a 2 + 2ab + b 2 = (a + b) (a + b) x 2 + 8x + 16 = (x + 4) (x + 4) x 2 +2(1)(4) + 4 2 = (x + 4) (x + 4) If you are having trouble recognizing the pattern, practice factoring like we did earlier.

11. 1) x 2 + 6x + 9 2) x 2 + 10x + 25

12. a 2 - 2ab + b 2 = (a - b) (a - b) x 2 - 14x + 49= (x - 7) (x - 7) x 2 – 2(1)(7) + 7 2 = (x - 7) (x - 7) Why do we ADD b 2 ?

13. 1) x 2 - 10x + 25 2) x 2 - 20x + 100

14. What if there is a coefficient in the front? 4x 2 – 12x + 9 What number squared is 4? 9? (2x - 3) Why is there a 12x in the middle? Check your answer!

15. 1) 4x 2 + 36x + 81 2) 25z 2 + 40z + 16

16. 1) 9n 2 – 42n + 49 2) 36d 2 – 60d + 25

17. Is 24g 2 -6 a difference of two squares? What should I do first? GCF = So…. 24g 2 – 6 = 6 (4g 2 – 1) = 6 (2g - 1) (2g + 1) Now factor using difference of squares!

18. 1)27x 2 + 90x + 75 2) 8z 2 - 64z + 128

19. Find the side length of the square! Area = 25r 2 - 30r + 9

20. 1. 18p 2 – 162 2. 50m 3 – 98m

21. a 3 + b 3 = (a + b)(a 2 – ab + b 2 ) 27x 3 + 1 = (3x) 3 + (1) 3 = (3x + 1)((3x) 2 – (3x)(1) + 1 2 ) = (3x + 1)(9x 2 – 3x + 1)

22. Example 1: 8k 3 + 729 Example 2: 343u 6 + 216

23. a 3 – b 3 = (a – b)(a 2 + ab + b 2 ) x 3 – 8 = (x) 3 - (2) 3 = (x – 2) (x 2 + (2)(x) + 2 2 ) = (x – 2) (x 2 + 2x + 4)

24. Example 1: 64x 3 – 27 Example 2: 125p 3 - 512

25. a 3 ± b 3 = (a [same sign] b)(a 2 [opposite sign] ab [always positive] b 2 )

26. Factor: c 10 – 30c 5 d + 225d 2

27. If 49x 2 – kx + 36 is a perfect square trinomial, what is the value of k?

28. Worksheet Start thinking about your test...it’s on TUESDAY!!!