1. Factoring Review

2. Factoring
The process of rewriting an equation or expression as the product of its factors
Example: x2 + 3x + 2 = (x + 2)(x + 1)
Most common form is the quadratic form: ax2 + bx + c, a ≠ 0

3. Factoring (when a = 1) ax2 + bx + c = (x + ___ ) (x + ___ )
multiply to equal c and add up to equal b
You can always check your answer by FOIL-ing!

4. Finding Factors of C Identify the value of c
On your calculator, go to the y= screen
Type C/X into y1
Go to the table
Any whole numbers (positive, non-decimal numbers) in the y1 column are factors of c

5. Example

6. Example #1

7. Example #2

8. Example #3

9. Your Turn: Complete problems 1 – 3 on the “Factoring Practice” handout
Check your answer by FOIL-ing!

10. 1. (x + 9)(x + 2) 2. (y – 7)(y + 5) 3. (g – 6)(g + 2)

11. Difference of Squares When we use it: Usually in the form ax2 – c
Both a and c are perfect squares (the square root of each number is a whole number)

12. Example #1

13. Example #2

14. Your Turn:
Complete problems 4 – 10 on the “Factoring Practice” handout
Remember to check your answer by FOIL-ing!

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

18. Example #1

19. Example #2

20. Example #3

21. Your Turn:
Complete problems 11 – 20 on the “Factoring Practice” handout
Don’t forget to check by FOIL-ing!

25. GCF (Greatest Common Factor)
When we use it: all the terms share 1 or more factors
Factoring out GCFs save us time!!!
4x2 – 196 = 0
(2x + 14)(2x – 14) = 0

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

27. Example #1

28. Example #2

29. Example #3

30. Your Turn:
Complete problems 17 – 27 on “Factoring Practice” handout

34. Warm-up (2 m)
20x6y7 + 12xy3 + 28x7y2
6x2 + 19x - 11

35. GCFs and The Welsh Method
Make sure you factor out any GCFs or the Welsh Method doesn’t work!!!

37. Your Turn:
Complete problems 28 – 33 on the “Factoring Practice” handout using the GCF and the Welsh Method

40. Picking the Correct Method
34. x2 + 10x + 16

41. Picking the Correct Method
35. 5t2 + 28t + 32

42. Picking the Correct Method

43. Your Turn:
Completely factor problems 36 – 44 on the “Factoring Practice” handout. In your solution, state the method(s) you used to completely factor the expression.