1. Factoring: Dividing Out
Divide OUT:
The LARGEST NUMBER you can divide ALL terms by
The SMALLEST POWER of a variable that exists in ALL terms
What you can divide out is a factor in front of ()
What remains when you divide out is a factor inside the ()
Check to see if the () can be factored more

2. Examples: Dividing Out
1. 2x⁵- 18x²
2. 3x³ - 12x² + 15x
3. 2x⁴ - 18x³

3. Factoring: Difference of Squares
2 terms
SUBTRACTION
Both terms have nice square roots (may need to divide out first).
Create 2 Factors
Square root of first term FIRST in each factor
Square root of second term SECOND in each factor
Each factor has a different operation between terms
(√first + √second)(√first - √second)

4. Examples: Difference of Squares

5. Examples: Divide Out & Difference of Squares
1. 2x⁵ - 18x³
2. 27x³ - 3x
3. 3x⁵ - 75x³

6. Factoring by Grouping 4 TERMS Separate into 2 Groups of 2 terms
Divide out of first pair
Divide out of second pair so the () has the SAME factor as the first pair did.
Create 2 factors
The SHARED FACTOR of the 2 groups
What was divided out of each pair
Check to see if either factor can be factored more!

7. Examples: Grouping
1. x³ - 3x² - 16x + 48
2. x³ + x² - x - 1

8. More Examples: Grouping
3. x³ + 7x² - 9x – 63
4. x³ - 7x² + 4x - 28