Factoring Review

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

Factoring (when a = 1)

ax2 + bx + c = (x + ___ ) (x + ___ )

multiply to equal c and add up to equal bYou can always check your answer by

FOIL-ing!

Finding Factors of C1. Identify the value of c2. On your calculator, go to the y= screen3. Type C/X into y14. Go to the table5. Any whole numbers (positive, non-

decimal numbers) in the y1 column are factors of c

Example

Example #1

24x11x2

Example #2

35x2x2

Example #3

12x7x2

Your Turn: Complete problems 1 – 3 on the “Factoring

Practice” handout Check your answer by FOIL-ing!

1. (x + 9)(x + 2)

2. (y – 7)(y + 5)

3. (g – 6)(g + 2)

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)

)cxa)(cxa(

cax2

Example #1

81h2

Example #2

144j49 2

Your Turn: Complete problems 4 – 10 on the “Factoring

Practice” handout Remember to check your answer by FOIL-ing!

4. 5.

6. 7.

8.

Factoring (when a ≠ 1):The Welsh Method

1. Multiply c and a2. Rewrite the expression with the new value for c3. Write (ax + )(ax + )4. Finish “factoring” the new expression5. Reduce each set of parentheses by any common

factors

Example #1

4y13y3 2

Example #2

2x5x3 2

Example #3

2g5g7 2

Your Turn: Complete problems 11 – 20 on the

“Factoring Practice” handout Don’t forget to check by FOIL-ing!

11. 12.

13. 14.

15. 16.

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

GCF (Greatest Common Factor) Steps:1. Identify any common factor(s) (including

the GCF)2. Factor out the common factor(s)3. Factor the remaining expression if possible

Example #1

x3x2x 23

Example #2

64x32x4 2

Example #3234 y21y24y3

Your Turn: Complete problems 17 – 27 on “Factoring

Practice” handout

17. 18.

19. 20.

21. 22.

23. 24.

25. 26.

27.

Warm-up (2 m)

1. 20x6y7 + 12xy3 + 28x7y2

2. 6x2 + 19x - 11

GCFs and The Welsh Method

4x14x12 2 Make sure you factor out any GCFs or the

Welsh Method doesn’t work!!!

Your Turn: Complete problems 28 – 33 on the

“Factoring Practice” handout using the GCF and the Welsh Method

28. 29.

30. 31.

32. 33.

Picking the Correct Method

34. x2 + 10x + 16

Picking the Correct Method

35. 5t2 + 28t + 32

Picking the Correct Method

16p2 – 9

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.

37. 38.

39. 40.

41. 42.

43. 44.