1. Removing Common Factors Difference of Two Squares Factoring: Puzzle Method Perfect Square Trinomials Sum or Difference of Two Cubes ( )( ) = 0 u 2 = constant x 2 +bx+ c = 0 (x + ) 2 =

2.  Objective is to get to a recognizable quadratic form & then to use one of your known tools. They are: a) Factoring to a pair of binomials: (…)(…) b) Extracting the Square: u 2 – c = 0 c) Completing the Sq: (x + ) 2 = d) Quadratic Formula  Approaches for Polynomials of degrees > 2 : 1. First, factor … simple & complex  hopefully to x 2 2. Let x 2 = u … substitute, simplify & solve    na

3. 1. 9 x 2 +18 x +81=0 2. 3 x 2 +27 x +60=0 3. 5 x 2 -65 x +210=0 4. 2 x 2 +10 x +12=0 5. 5 x 3 +25 x 2 +30 x = 0 6. 2 x 3 -4 x 2 -48 x =0 7. 3 x 4 -24 x 3 +21 x 2 =0 8. ½x 3 +3 x 2 +4 x =0 9. ½x 3 +2 x 2 -6 x =0 10. ½x 3 +7 x 2 +24 x =0 11. 2 x 2 -162=0 12. 3 x 3 -27 x =0 13. 5 x 3 -125 x =0 When only Simple Factoring is Needed

4. 1 st Hint: Let u = x 2, & substitute u for x !! 2 nd Hint: See page 134 !

5. 1. x 3 – 2 x 2 + x – 2 = 0 2. x 3 – 3 x 2 + 2 x – 6=0 3. x 3 – x 2 + 2 x – 2 = 0 4. x 3 + 3 x 2 + 4 x + 12=0 5. x 3 – x 2 – 4 x + 4=0 When Complex Factoring is Needed

6. What would your approach be ?? Solve by ?? a) Factoring: (…)(…) b) Extracting the Square: u 2 – c 2 c) Completing the Sq: (x + ) 2 = d) Quadratic Formula