1. Factoring Review
AMT

2. Step1. Look for GCF and factor it out to the front
1. 7x + 49
2. 8ax – 56a
3. t2h + 3t
4. x + x2y + x3y3
5. 4a 2b2 + 16ab + 12 a

3. Factoring by grouping (only do this when there are 4 terms without a GCF)
1. Group the first two terms and the last two terms
2. Pull out a GCF for each group
3. The ( ) should be the same
4. Final answer is the ( ) that are the same and the GCF’s in the second ( )

4. Examples 6-8 6. x2 + 3x + x + 3 7. 2x2 + 2x + 3x + 3

5. Solving
1. Get everything on one side so the equation is set = 0 then factor just like you normally would.
2. Set each factor equal to 0 and solve for the variable

6. Examples 9-11
9. x(x – 8) = 0
10. x2 – 5x = 0
11. 3x2 = 6x

7. Trinomials
1. Factors of the last term that + or – to give you the middle term
2. Last term + and middle term - ( - )( - )
Last term + and middle term + ( + )( + )
Last term – means ( ) ( )
Larger factor goes with the sign of the middle term

8. Examples 12-24 12. t2 + 8t + 12 13. p2 + 9p + 20 14. n2 + 3n – 18
15. y2 – 5y - 6

9. 16. x2 + 4x -12
17. w2 – w – 6
18. x2 – 8x + 15
19. t2 – 15t + 56

10. 20. x2 – 6x + 8 = 0
21. m2 + 5m + 6 = 0
22. y2 – 2y -24 = 0
23. h2 + 2h = 35
24. n2 – 36 = 5n

11. More Trinomials “Beef” it up and “Cut” the fat
Same rules as earlier but now we want factors of the product of the first and last terms.
Cut out the GCF at the end

12. Examples 25-35 25. 2x2 + 5x + 2 26. 2x2 + 9x – 9 27. 2x2 + x – 1

13. 30. 3a a + 63
31. 2x2 + 7x + 3 = 0
32. 3x2 – 7x + 2 = 0

14. 33. 6x2 + 8x + 2 = 0
34. 9x2 + 18x – 12 = 6x
35. 10x2 – 15x = 8x – 12

15. Differences of Squares
Factor into ( ) ( - )
Take the square root of each term

16. Examples 36-42
36. 1 – 49d2
37. t2 – 81u2
38. 64x2 – 9y2
39. 20x2 – 5y2
40. 16x2 – 9 = 0
41. 36b2 – 49 = 0
42. n2 – 9 = 0