1 / 22

Factoring-Special Cases

Factoring-Special Cases. February 15 th , 2012. Warm Up. Factor the following. Determine whether to factor by GCF, Easy Trinomial (ET), Hard Trinomial (HT), Factoring By Grouping (FBG )—or a combination! Write to the side the methods you used! First example is done…

derora
Download Presentation

Factoring-Special Cases

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. Factoring-Special Cases February 15th, 2012

  2. Warm Up Factor the following. Determine whether to factor by GCF, Easy Trinomial (ET), Hard Trinomial (HT), Factoring By Grouping (FBG)—or a combination! Write to the side the methods you used! First example is done… 1) 20x2 - 115x - 30 __GCF__HT_ 2) x2 + 4x – 96 ______ ______ • 14a2 b - 63a5 b6______ ______ 4) 12x3 +3x2 +20x +5______ ______

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

  4. Using what you know… • If given x2 – 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. Difference of Two Squares a2 - b2 = (a - b) (a + b) x2 - 22 = (x - 2) (x + 2) x2 – 4 = (x - 2) (x + 2) This only works for the DIFFERENCE, not sum/addition!

  6. Example 1 Factor x2 - 9 = (a - b) (a + b) What number squared is 9? So… (x - 3) (x + 3) Check your answer by FOIL or box!

  7. Example 2 • What if there is a coefficient in the front? 4x2 – 25 It works the same way! What number squared is 4? 25? (2x - 5) (2x + 5)

  8. You try! 1) x2 – 144 2) w2 – 64 3) 16m2 – 49 4) 9k2 – 400

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

  10. Perfect-Square Trinomials: + a2 + 2ab + b2 = (a + b) (a + b) x2 + 8x + 16 = (x + 4) (x + 4) x2 +2(1)(4) + 42 = (x + 4) (x + 4) If you are having trouble recognizing the pattern, practice factoring like we did earlier.

  11. Examples 1) x2 + 6x + 9 2) x2 + 10x + 25

  12. Perfect-Square Trinomials: - a2 - 2ab + b2 = (a - b) (a - b) x2 - 14x + 49= (x - 7) (x - 7) x2 – 2(1)(7) + 72 = (x - 7) (x - 7) Why do we ADD b2?

  13. Examples 1) x2 - 10x + 25 2) x2 - 20x + 100

  14. Example • What if there is a coefficient in the front? 4x2 – 12x + 9 What number squared is 4? 9? (2x - 3) (2x - 3) Why is there a 12x in the middle? Check your answer!

  15. Examples 1) 4x2 + 36x + 81 2) 25z2 + 40z + 16

  16. You try! 1) 9n2 – 42n + 49 2) 36d2 – 60d + 25

  17. Example • Is 24g2 -6 a difference of two squares? • What should I do first? • GCF = • So…. 24g2 – 6 = 6 (4g2 – 1) = 6 (2g - 1) (2g + 1) Now factor using difference of squares!

  18. You try! • 27x2 + 90x + 75 2) 8z2 - 64z + 128

  19. Example • Find the side length of the square! Area = 25r2 - 30r + 9

  20. Challenge Question #1 Factor: c10 – 30c5d2 + 225d

  21. Challenge Question #2 If 49x2 – kx + 36 is a perfect square trinomial, what is the value of k?

  22. Homework • Workbook pg. 247 Factoring Special Cases • COMPLETE ALL ODDS! • Workbook pg. 248 • Choose any 5 questions between #26-43

More Related