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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