Drill #25Simplify each expression.
2
2
43325342
)2)(1(.3
)13(.2
)6
52
4
3(8.1
xx
x
yxyxyxyx
Drill #26
Find the GCF of the following monomials:
Factor each polynomial using the GCF:
246.4
1593.3
6216.2
20,10,5.1
22
5432
2
xyz
yxyx
cbabcba
xxyx
Drill #27
Factor each polynomial using the GCF:
Factor by Grouping
Factor the following trinomials:
3612.4
103.3
1326.2
105.1
2
2
2
2
xx
xx
aabba
xyxyzyx
Drill #28
Factor each polynomial using the GCF:
Factor the following trinomials:
1596.4
4213.3
324.2
151064.1
2
22
2
2
xx
yxyx
xx
aaxxx
Drill #52
Factor each polynomial :
22
2
2
2
23.4
482.3
86.2
3613.1
yxyx
xx
xx
xx
Drill #53
Factor each polynomial :
22
22
2
2
4116.4
96.3
99100.2
276.1
yxyx
yxyx
xx
xx
Drill #54
Factor each polynomial :
673.3
2510.2
488.1
2
22
2
xx
yxyx
xx
GCF: Monomials
To find the GCF of two monomials:
• Find the GCF of the coefficients
• For each common, the GCF is the common variable with the lower degree
• Combine the GCF of the coefficients and the variables together to make one term
322 72,16: xyzzxyex
GCF Examples: 8-1 Study Guide (even problems)
Classwork: 8 – 16 (EVEN)
Factor Polynomials: GCF
To factor polynomials:
• Find the GCF of all terms in the polynmial
• Use the distributive property to undistribute GCF
• Factor the remaining expression (if possible)
Factor Polynomials: Factor by Grouping
To factor a polynomial by grouping (4 or 6 terms)
• GCF Factor the first two (three) terms
• GCF factor the last two (three) terms
• If there is a common factor between them, factor it (undistribute)
Ex: 6ax + 3ay + 2bx + by
Factoring Polynomials*Always GCF factor 1st!!!!!!!
1. GCF Factoring
2. Two Terms:
- Difference of Squares
- Difference of Cubes
- Sum of Cubes
3. Three Terms:
Trinomial Factoring
4. Four or More Terms
Factor by Grouping
Multiply binomials:
What is ( x + 2) (x + 5)?
cbxx 2
Trinomial Factoring: Three Terms*
Factoring:
Where m + n = b
and m(n) = c
To factor trinomials make a factor sum table!
cbxx 2
))((2 nxmxcbxx
Trinomial Factoring Examples*
Example 1a, b: 8-3 Study Guide
Classwork: 2-8 (even)
Factoring Trinomials with 2 2nd Degree Terms
Example: #20
22 127: yxyxEx
Trinomial Factoring: Three Terms*: Factor by Grouping Method
Factoring:
1. GCF factor (if possible)2. Find factors m,n of a*c (that add up to b)3. Change bx to mx + nx4. Factor by grouping
Ex: To factor trinomials make a factor sum table!
cbxax 2
18152 2 xx
Trinomial Factoring: Three Terms*: Illegal Method
Factoring:
1. GCF factor (if possible)2. Multiply ac and rewrite as 3. Factor to (x + m)(x + n)4. Divide m and n by a and reduce fractions5. The denom. of any fractions that don’t reduce
become coefficients
To factor trinomials make a factor sum table!
cbxax 2
acbxx 2
Trinomial Factoring Examples*
Example 1, 2: 8-4 Study Guide
Classwork:
8-4 Study Guide #2 – 8 (even)
FOIL the following binomials
What is (x – 4 )(x + 4)
Two Terms: Factoring Difference of Squares*
To factor difference of squares:
Examples:
22
2
22
22
94
9
))((
yx
x
yx
bababa
Two Terms: Factoring Sum of Cubes*
To factor sum of cubes:
Example:
333
3
2233
648
27
))((
zyx
x
babababa
Two Terms: Factoring Difference of Cubes*
To factor difference of cubes:
Examples:
3
3
2233
216125
8
))((
x
x
babababa
Classwork: 6-5 Study Guide
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