1. Aim: How do we factor polynomials completely? Do Now: Factor the following 1. 2x 3 y 2 – 4x 2 y 3 2. x 2 – 5x – 6 3. x 3 – 5x 2 – 6x

2. x 3 – 5x 2 – 6x= x(x 2 – 5x – 6)= x(x – 6)(x + 1) To factor a polynomial, GCF is always the first thing to think about. If there is no GCF among the terms, then try the other two methods (trinomial form or difference of two squares) To factor a polynomial completely, we usually factor GCF first then follow by either trinomial form or difference of two squares

3. 3x 3 – 9x 2 + 6x = 3x(x 2 – 3x + 2) = 3x(x – 2)(x – 1) Look for GCF Factor the trinomial into two binomials 5x 3 y 2 – 15x 2 y 2 – 20xy 2 GCF is 5xy 2 = 5xy 2 (x 2 – 3x – 4) = 5xy 2 (x – 4)(x + 1) Factor the trinomial into two binomials

4. 6x 2 – 24 Factor the GCF 6 = 6(x 2 – 4) = 6(x – 2)(x + 2) Factor by difference of two squares 2x 3 – 50xy 2 = 2x(x 2 – 25y 2 ) Factor the GCF 2x = 2x(x – 5y)(x + 5y) Factor by difference of two squares

5. Factor the following completely 1. 36x 3 – 72x 2 – 108x 2. 45x 2 – 5y 2 3. x 3 y – 8x 2 y – 9xy 4. x 4 – 16