1. Lesson 5-4 & 5-5: Factoring Objectives: Students will:
Factor using GCF
Identify & factor square trinomials
Identify & factor difference of two squares

2. Day 1
Trinomials

3. factor flow chart If there is a GCF factor it out!!!!!! Ex: 2x + 8
Remember:
Number of exponent tells you number of
Factors/ Solutions/ Roots/ Intercepts
x1 = 1 factor
x2 = 2 factors
x3 = 3 factors
x4 = 4 factors and so on…..
If there is a GCF factor it out!!!!!!
Ex: 2x + 8
2(x + 4)
Binomial
(2 terms)
Trinomial
(3 terms)
Polynomial
(4 terms)
Is it a difference of squares or cubes ?
A2- B2 or A3±B3
ex: 4x2 – 25 or x3 - 64
Done No
Difference of Squares (DS)
A2- B2 = (A +B )(A – B)
Ex: 4x2 – 25 = (2x + 5)(2x - 5)
Repeat with (ax-b) if possible
Difference (or sum) of Cubes
(A3 – B3) = (A - B)(A2 +AB + B2)
Or (A3 + B3) = (A + B)(A2 - AB + B2)
(then factor trinomial if possible)
Ex: x3 – 64 = (x – 4)(x2 + 4x + 16)
Is it a Perfect Square Trinomial?
A2 ± 2AB + B2
ex: 4x2-20x +25
(2x-5)2
PST
A2 +2AB+B2 = (A + B)2
Or A2 -2AB+B2 = (A - B)2
Ex: 4x2 –20x +25 = (2x - 5)2
yes
Find
Write out factors
If a=1
If a≠1
Rewrite as four terms
Factor by:
Grouping Or
Undo foil
( )( ) or box ac b

4. The reverse of multiplying 2x(x+3) = 2x2 + 6x So: 2x2 + 6x =
Factoring
The reverse of multiplying
2x(x+3) = 2x2 + 6x
So: 2x2 + 6x =
Look for GCF of all terms → numbers & variables
► Reverse distribute it out → DIVISION
Example 1 Factor 6u2v3 – 21uv2 What is the GCF?
Pull out GCF (divide both terms)
3uv2
3uv2(2uv - 7)

5. Make Sure Polynomial is in descending order!!!!!!!! 3 Methods
Factoring 4-term
Make Sure Polynomial is in descending order!!!!!!!!
3 Methods
Reverse FOIL
F O I L
x2 + 5x + 4x + 20
( )( )
REMEMBER: ALWAYS FACTOR A GCF 1st IF YOU CAN
Find GCF of first two terms- fill first spot
Find what makes up ( F) and fill in first spot in other factor already have x so need another x
Move to outside (O) already have x so need + 5
Move to inside (I) already have x so need + 4
Check last (L) 4x5 =20 so done!! x
+ 4 x
+ 5

6. Foil Box + 5x + 20 + 4 x2 + 5x + 4x + 20 ( x + 5)(x + 4) x + 5 x F x2

7. It’s the same either method!!
B) Factor by grouping
Find GCF of first two terms- and factor out
Find GCF of second two terms- and factor out
What is in parenthesis should match –so factor it out
Write what is left as other factor
x2 + 5x + 4x + 20
x( x + 5 )
+ 4(x + 5)
(x + 5)
(x - 4)
It’s the same either method!!
I like the FOIL method. What do you think????

8. So to factor we are unFOILing!!
ax2 + bx + c – A General Trinomial
Where does middle term come from?
(x + 2)(x + 3) = x2 + 3x + 2x + 6
(2x + 4)(x – 3) =
2x2 - 6x + 4x – 12
2x2 - 2x - 12
So to factor we are unFOILing!!

9. Steps for General Trinomial Factoring
1) Factor out GCF (always first step)
2) Find product ac that add to b table (to find O and I)
3) Write middle term as combo of factors ( 4 terms)
4)Unfoil or by grouping
Example 1:
x2 + 7x + 12
F O I L
( )( ) 12
1) no GCF
x2 + 4x + 3x + 12 2) ac
1*12 b 7 x
+ 3 x
+ 4
1*12 13
2*6 8
3*4 7

10. TRY
Example 2 Factor x2 – 5x – 24
Example 3 Factor x2 – 12x + 27

11. EX 4) Harder One 6x2 – 5x – 4 -8x -24 6x2 + 3x - 4 F O I L ( ) ( ) 3x
( ) ( ) 3x
- 4 2x
+ 1
GCF of first 2

12. Factor: -7a + 6a2 -10

13. Factor: x – x2

14. Assignment (day 1)
5-5/227/ e

15. Day 2

16. Factoring Perfect Squares, Difference of Square,
Look back at the forms for each of these from Lesson 5-3
Factor the following:
Ex 1: x2 – 8x Perfect Square Trinomial so
Ex 2: 9x2 – 16y Difference of squares so
(x - 4)2
(3x + 4y)(3x – 4y)

17. Ex 3:
Factor 8x2 – 8y2
Don’t forget GCF!

18. Trick: Ex 4: Combo perfect square trinomial and difference of squares
x2 – 2xy + y2 – 25
(x-y)2 - 25
((x-y) + 5)((x-y) – 5)
Apply PST
Now apply DS

19. Ex 5:
Factor:

20. Marker Board pg 21 33 41 51

21. ASSIGNMENT
5-4/ /18-62e, e

22. Day 3
Sum or Difference of cubes

23. Review Cubing Binomials
(a+b)3= (a+b)(a2 +2ab+b2)
a3 +3a2b+3ab2+b3
(similarly for (a-b)3)

24. Example 1: (a3 + b3) (a3 + b3)= ( a+b)(a2-ab+b2)
Notice all the middle terms cancelled out like DS.
What were the terms that cancelled?
What are the factors?
Example 1:
(a3 + b3) a2
-ab
+ b2 a3
-a2b
ab2 a +b
a2b
-ab2 b3
(a3 + b3)= ( a+b)(a2-ab+b2)
Is the remaining trinomial factorable?

25. Ex 2: Factor 27x3-8y3 -8y3 A3 – B3 = (A-B)(A2 + AB+ B2)
27x3-8y3=(3x-2y)(9x2+6xy+4y2)
A3 – B3 = (A-B)(A2 + AB+ B2)

26. Ex 3: Factor x3 + 64

27. Formulas
A3 – B3 = (A-B)(A2 + AB+ B2)
A3 + B3 = (A+B)(A2 - AB+ B2)

28. Factor : 125x3 +1

29. Marker Board pg 227 1 13 19