Factoring: Dividing Out

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Presentation transcript:

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

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

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)

Examples: Difference of Squares

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

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!

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

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