1 / 64

Factoring Trinomials

Chapters 9.3 and 9.4. Factoring Trinomials. Factoring Trinomials. Lesson Objective: Students will know how to use the box method to factor a trinomial. Factoring Trinomials. Review. Example: Solve (x + 3)(x + 2) Remember we use the box method to solve this problem. Factoring Trinomials.

navid
Download Presentation

Factoring Trinomials

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. Chapters 9.3 and 9.4 Factoring Trinomials

  2. Factoring Trinomials • Lesson Objective: • Students will know how to use the box method to factor a trinomial

  3. Factoring Trinomials Review • Example: Solve (x + 3)(x + 2) • Remember we use the box method to solve this problem

  4. Factoring Trinomials Review • Solve: (x + 3)(x + 2) x +3 x x x2 * x x 3x * 3 6 2x * x 2 * 3 +2 2

  5. Factoring Trinomials X + 3 +2 x x2 3x 2x 6 x2 + 5x + 6

  6. Factoring Trinomials • Today we’re going to learn how to do this in reverse

  7. Factoring Trinomials • Example 1: Factor x2 + 7x + 12 • We’re going to use the box method to factor this problem

  8. Factoring Trinomials • Factor x2 + 7x + 12 • Usually we put the problem on the outside, but we were given the answer instead! • So we need to find the numbers on the outside

  9. Factoring Trinomials • Factor x2 + 7x + 12 • In order to find our answer we had to take the numbers from inside the square + 7x + 12 X2

  10. Factoring Trinomials • Factor x2 + 7x + 12 • Let’s put everything back into the box X2 12 + 7x + 12 X2

  11. Factoring Trinomials • Factor x2 + 7x + 12 • As you can see, we have one number and 2 spots for it • We have to split the 7x into 2 numbers X2 12 + 7x + 12 X2

  12. Factoring Trinomials • Factor x2 + 7x + 12 • Start by multiplying the 12 and x2 • = 12x2 X2 12 + 7x + 12 X2

  13. Factoring Trinomials • We’re going to have to set up 2 tables

  14. Factoring Trinomials • In the first table we put products that multiply to 12x2 1x 12x * 6x 2x * 3x 4x *

  15. Factoring Trinomials • In the second table we add instead of multiply to get the number in the middle 1x 12x 1x + 12x * + 6x 2x 6x 2x * + 3x 4x 3x 4x *

  16. Factoring Trinomials • Notice the 3x and 4x work for both tables 1x 12x 1x + 12x * + 6x 2x 6x 2x * + 3x 4x 3x 4x *

  17. Factoring Trinomials • Therefore, these are the two numbers that fill in the box 1x 12x 1x + 12x * + 6x 2x 6x 2x * + 3x 4x 3x 4x *

  18. Factoring Trinomials • It doesn’t matter where each one goes, so put them both in the box X2 3x 4x 12 + 7x + 12 X2

  19. Factoring Trinomials x 3 • We can use the Greatest Common Factor to get the numbers on the outside • The GCF of x2 and 4x is x • The GCF of 3x and 12 is 3 x X2 3x 4 4x 12 + 7x + 12 X2

  20. Factoring Trinomials x 3 • We can then put the numbers on top together for one parenthesis • The side is the other parenthesis x X2 3x 4 4x 12 (x + 4) (x + 3) + 7x + 12 = X2

  21. Factoring Trinomials Let’s try that again! • Factor: x2 + 3x – 4 • Start with the box

  22. Factoring Trinomials • Factor x2 + 3x – 4 • Let’s put everything back into the box X2 – 4 + 3x – 4 X2

  23. Factoring Trinomials • Factor x2 + 3x + 12 • Start by multiplying the -4 and x2 • = -4x2 X2 – 4 + 3x – 4 X2

  24. Factoring Trinomials • Set up your two tables 1x -4x 1x + -4x * + 4x -1x 4x -1x * + 2x -2x 2x -2x *

  25. Factoring Trinomials • We see that -1x and 4x works for both tables so those are our numbers 1x -4x 1x + -4x * + 4x -1x 4x -1x * + 2x -2x 2x -2x *

  26. Factoring Trinomials • It doesn’t matter where each one goes, so put them both in the box X2 -1x 4x -4 + 3x – 4 X2

  27. Factoring Trinomials x -1 • We can use the Greatest Common Factor to get the numbers on the outside • The GCF of x2 and 4x is x • The GCF of -1x and -4 is -1 x X2 -1x 4 4x -4 + 3x – 4 X2

  28. Factoring Trinomials x -1 • Always take the sign closest to the number on the outside! x X2 -1x 4 4x -4 + 3x – 4 X2

  29. Factoring Trinomials x -1 • We can then put the numbers on top together for one parenthesis • The side is the other parenthesis x X2 -1x 4 4x -4 (x + 4) (x – 1) + 3x – 4 = X2

  30. Factoring Trinomials Practice • Factor the following: 1. x2 + 8x + 12 2. x2 + 18x + 32 3. x2 – 4x + 4 4. x2 – 7x + 6 5. x2 + 10x + 25

  31. Factoring Trinomials Practice • Factor the following: 1. x2 + 8x + 12 2. x2 + 18x + 32 (x + 6)(x + 2) (x + 16)(x + 2) 3. x2 – 4x + 4 4. x2 – 7x + 6 (x – 6)(x – 1) (x – 2)(x – 2) 5. x2 + 10x + 25 (x + 5)(x + 5)

  32. Factoring Trinomials x2 + 6x = 7 • Solve: • If you see an x2 and an equals sign, you have to get everything on one side of the equation • Now we need to factor the left side -7-7 x2 + 6x – 7 = 0

  33. Factoring Trinomials • Let’s put everything back into the box • Multiply -7 and x2 • = -7x2 X2 – 7 x2 + 6x – 7 = 0

  34. Factoring Trinomials • Set up your two tables -1x 7x -1x + 7x *

  35. Factoring Trinomials • We see that -1x and 7x works for both tables so those are our numbers -1x 7x -1x + 7x *

  36. Factoring Trinomials • Plug in the two numbers X2 -1x – 7 7x x2 + 6x – 7 = 0

  37. Factoring Trinomials x -1 • Find the GCF to put on the outside of the box x X2 -1x 7 – 7 7x x2 + 6x – 7 = 0

  38. Factoring Trinomials x -1 • Replace the equation with your answer x X2 -1x 7 – 7 7x (x + 7) (x – 1) x2 + 6x – 7 = 0

  39. Factoring Trinomials (x + 7) (x – 1) = 0 • Just a reminder: x*y = 0 means that either x or y has to be zero! • We must set both parenthesis equal to zero and solve x + 7 = 0 x – 1 = 0 -7-7 +1+1 x = -7 x = 1

  40. Factoring Trinomials Practice • Factor the following: 1. x2 + 7x + 12 = 0 2. x2 + 10x = -16 3. x2 + 6 = 5x 4. x2 – 5x – 6 = 0 5. x2 + 10x – 24 = 0

  41. Factoring Trinomials Practice • Factor the following: 1. x2 + 7x + 12 = 0 2. x2 + 10x = -16 x = -3 and -4 x = -8 or -2 3. x2 + 6 = 5x 4. x2 – 5x – 6 = 0 x = 6 or -1 x = 2 or 3 5. x2 + 10x – 24 = 0 x = -12 or 2

  42. Factoring Trinomials 2x2 + 15x + 18 • Example 4: Factor • We’re going to work this like the other problems

  43. Factoring Trinomials • Start with the box! • Multiply 18 and 2x2 • = 36x2 2x2 18 2x2 + 15x + 18

  44. Factoring Trinomials • Set up your two tables 1x 36x 1x 36x + * 2x 18x 2x 18x + * 3x 12x 3x 12x + *

  45. Factoring Trinomials • 3x and 4x works for both, so those are our numbers 1x 36x 1x + 36x * 2x 18x 2x 18x + * 3x 12x 3x 12x + *

  46. Factoring Trinomials • Plug in the two numbers 2x2 12x 18 3x 2x2 + 15x + 18

  47. Factoring Trinomials x 6 • Find the GCF to put on the outside of the box 2x 2x2 12x 3 18 3x 2x2 + 15x + 18

  48. Factoring Trinomials x 6 • We can then put the numbers on top together for one parenthesis • The side is the other parenthesis 2x 2x2 12x 3 18 3x 2x2 + 15x + 18 (2x + 3) (x + 6)

  49. Factoring Trinomials • Example 5: Factor: • Plug them into the box • Multiply -6 and 2x2 • = -12x2 2x2 + 3x – 6 2x2 -6 2x2 + 3x – 6

  50. Factoring Trinomials • Set up your two tables -1x 12x -1x + 12x * -2x 6x -2x 6x + * -3x 4x -3x 4x + *

More Related