1. Factoring Polynomials: Part 1
GREATEST COMMON FACTOR (GCF) is the product of all prime factors that are shared by all terms and the smallest exponent of any variable common to all terms.
LARGEST NUMBER that can divide all terms
SMALLEST EXPONENT of common variables to all terms
Examples:
1) 15, 16
15 = 3 • 5
16 = 2 • 2 • 2 • 2
GCF = 1
2) 72, 36, 42
72 = 2 • 2 • 2 • 3 • 3
36 = 2 • 2 • 3 • 3
42 = 2 • 3 • 7
GCF = 2 • 3 = 6
3) 6x2y6, 32x3y4, 10x5y3
6x2y6 = 2 • 3 • x2 • y6
32x3y4 = 2 • 2 • 2 • 2 • x3 • y4
10x5y3= 2• 5 • x5 • y3
GCF = 2 • x2 • y3 = 2x2y3

2. Factoring a polynomial by its GREATEST COMMON FACTOR (GCF)
“Reverse the Distributive Property”
STEP #1: Find the GCF for all terms of polynomial
STEP #2: Find Factored Polynomial by dividing all terms by GCF
STEP #3: Factored Form = (Step #1)(Step #2)
Exp 1: 10x3z – 25x6y
Step #1: GCF = 5x3
Step #2:
Step #3: 5x3(2z – 5x3y)
Exp 2: 14a3b2 + 28a5b5 + 35a2b4
Step #1:
Step #2:
Step #3:

3. FACTORING PRACTICE #1: Factor by the GCF
(1) 72a3 – 50ab2 (2) 6y5 + 30y4 + 24y3
(3) 10x2 – 45x (4) 2xy – 10x
(5) 5x2y2 – 15x2y (6) 12x2 – 42xy + 9y2

4. [1] Difference of Squares
Factoring Polynomials: Part 2
Special Binomial (2 Term) Factoring Techniques
[1] Difference of Squares
MEMORIZE!!!
EXP#1:
EXP#2:
EXP#3:

5. FACTORING PRACTICE #2: Difference of Squaresb) c) d) e) f)

6. (5x+ 3) (2x + 1) Factoring Polynomials: Part 3 4 – Term Polynomials
STEP #1: Check for GCF of entire polynomial
STEP #2: Factor by Grouping
Split polynomial: FIRST two terms and the LAST two terms.
FACTOR the GCF from both sides of split
Check for negative and positive sign agreement
Factored Form: (1st GCF + 2nd GCF) (factored polynomial)
Algebraic Example
Example: 10x2 + 5x + 6x + 3
GCF = 5x
GCF = 3
5x(2x + 1) + 3(2x + 1)
a is first GCF and d is second GCF
(5x+ 3) (2x + 1)

7. FACTORING PRACTICE #5: Factoring by Groupingd)

8. e) f) g) h)