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 =

 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

1. 9 x x +81= x x +60= x x +210= x x +12= x x x = x 3 -4 x x = x x 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 x = x = x x = x x =0 When only Simple Factoring is Needed

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

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

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