Factoring out the GCF

Greatest Common Factor The greatest common factor (GCF) is the product of what both items have in common. Example:18xy, 36y 2 18xy = 2 · 3 · 3 · x · y 36y 2 = 2 · 2 · 3 · 3 · y · y GCF = = 18y 2 · 3 · y

What is factoring?

Example: Factor:12a2 + 16a = 2·2·3·a·a + 2·2·2·2·a = 2 · 2 · a (3·a + 2·2) = 4a (3a + 4) You can check by distributing. 1. Factor each term. 2. Pull out the GCF. 3. Multiply.

Now you try! Example 1: 15x + 25x 2 Example 2: 12xy + 24xy 2 – 30x 2 y 4 = 6xy(2 + 4y – 5xy 3 ) = 5x(3 + 5x)

Factoring by Grouping

Example: Factor:5xy – 35x + 3y – 21 (5xy – 35x) + (3y – 21) = (5·x·y – 5·7·x)+ (3·y – 3·7) = 5·x (y – 7)+ 3 (y – 7) = 5x (y – 7)+ 3 (y – 7) = (5x + 3)(y – 7)

Example: Factor:5xy – 35x + 3y – 21 (5xy – 35x) + (3y – 21) = 5x (y – 7)+ 3 (y – 7) = (5x + 3)(y – 7) 1. Group terms with ( ). 2. Pull out GCF from each group. 3. Split into factors.

Notes - What is in parentheses MUST be the same!! - Grouping only works if there are 4 terms!!

Now you try! Factor. Example 1:5y 2 – 15y + 4y - 12 Example 2:5c – 10c 2 + 2d – 4cd