1. Review: Factoring

2. Factors Remember that “factors” of a number are the numbers that can be multiplied to get that number. Factors of 20 are 1 and 20, 2 and 10, 4 and 5. Factors of 4x are x and 4, 2x and 2, 4x and 1. Factors of 6x 2 are x 2 and 6, x and 6x, 2x and 3x.

3. Greatest Common Factor When “factoring an expression”, look for the greatest factor that they have in common. Examples: 2a + 8 2 is the greatest common factor y 2 – 9y y is the greatest common factor 16x 2 – 72xy 8x is the greatest common factor

4. Factoring an Expression After the GCF is identified, “take it out” of the expression. Examples: 2a + 8 = 2(a + 4) y 2 – 9y = y(y – 9) 16x 2 – 72xy = 8x(2x – 9y) Use the distributive property to make sure you are correct!

5. Factoring More Complicated Expressions If there are no common factors (or all common factors have already been “removed”) and the expression is still not simplified, you may need to “un-FOIL” the expression. x 2 + 7x + 12 No common factors… …but factors of 12 are 1 and 12, 2 and 6, 3 and 4… …and 3 + 4 is 7… (x + 3)(x + 4) Multiply out (FOIL) to make sure you are correct!

6. Difference of Squares When an expression is in the form a 2 – b 2, it can be factored following this pattern: (a – b)(a + b)

7. Difference and Sum of Cubes When an expression is in the form a 3 – b 3, it can be factored following this pattern: (a – b)(a 2 + ab + b 2 ) When an expression is in the form a 3 + b 3, it can be factored following this pattern: (a + b)(a 2 – ab + b 2 )