1. U7D6 Have out: Bellwork: pencil, red pen, highlighter, GP notebook,
Factor completely across the rationals. Be sure to look for any greatest common factor first! 1) 2) 3) –4 –3 35 12 +1 5 7 –4 +3 +2 +3
total:

2. Multiply the following together using a generic rectangle.b) x2
+ 2 a
+ b x c x3
+2x ac bc
+ 5
+5x2
+10
+ d
+ ad
+bd
What if you were given the answers above, but you needed to get back to the original problem. How would you “undo” the answer? Try _________!
factoring
However, diamond problems will not help because we are not working with __________.
trinomials

3. Group factoring 4
_______________ – when polynomials have ___ or more terms, it may be possible to factor these polynomials by __________ the terms in ______ to help with factoring.
grouping
pairs
a(b + c) =
ab + ac
Recall the distributive property: _________________. This will help us with group factoring.
Example #1: Factor
Group
Step 1: _______ pairs of terms that have a ________ monomial.
common
Step 2: Factor the _____ from each group.
GCF
Step 3: Notice that _____ is a common factor.
c + d
distributive
Step 4: Use the ___________ property to factor out ______.
c + d

4. Example #2 – 3: Factor completely using group factoring.2) 3)
Rewrite in descending order

5. Practice: Factor completely using group factoring.b)

6. Multiply the following together using a generic rectangle.b) x2
+ xy
+ y2 x2
– xy
+ y2 x x3
+ x2y x
+xy2 x3
– x2y
+xy2
– y
–x2y
–xy2
– y3
+ y
+x2y
–xy2
+ y3

7. What patterns do you notice?
All the middle terms cancel out. The only terms left are cubes.
The previous patterns lead us to the factoring method of _________________________.
Sum and Difference of Cubes
Sum:
Difference:
 Notice how the first factor almost matches the sum or difference of cubes.
 Notice that the first and last terms of the second factor are squared.
 Notice how the signs are different in the first factor and the middle term of the other factor.

8. Examples: Use the patterns above to factor the following:
( )( ) x
+ 4 x2
– 4x
+ 42
( )( ) y
– 3 y2
+ 3y
+ 32

9. (2x)2 2x + y – 2xy + y2 3a – 4b (3a)2 + 3a●4b + (4b)2
Examples: Use the patterns above to factor the following: c) d)
(2x)2
( )( ) 2x
+ y
– 2xy
+ y2
( )( ) 3a
– 4b
(3a)2
+ 3a●4b
+ (4b)2

10. Examples: Use the patterns above to factor the following:
– 5xy
( )( ) x
– 2 x2
+ 5y
+ (5y)2
+ 2x
( )( )
+ 22

11. We can prove that the rule always works for the Difference of Cubes.
Let a and b be any number, then:
zero
Add “______”
group
Use ______ factoring and factor the ______from each group
GCF
difference of squares
Use __________________ to factor ________
a – b
Notice that ______ is a common factor.
distributive
Use the ___________ property to factor out ______.
a – b
A similar proof can be given for the Sum of Cubes.

12. After the quiz, work on the rest of the packet.
Quiz Time
Clear your desk except for a pencil, highlighter, and a NON-GRAPHING calculator!
After the quiz, work on the rest of the packet.