Factoring out the GCF

Greatest Common FactorThe greatest common factor (GCF) is

the product of what both items have in common.

Example: 18xy , 36y2

18xy = 2 · 3 · 3 · x · y 36y2 = 2 · 2 · 3 · 3 · y · y

GCF =

= 18y2 · 3 · 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 + 25x2

Example 2:12xy + 24xy2 – 30x2y4

= 6xy(2 + 4y – 5xy3)

= 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: 5y2 – 15y + 4y - 12

Example 2: 5c – 10c2 + 2d – 4cd