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Strategies of factoring, Greatest common factor is the first step when…

- - - - 4x³-15+20x²-3x= 4x²(x+5)-3x(x+5)= (x+5)(4x²-3x)
        
        10a4 +15a² -25a-30= 5 ( 2a4 +3a²) -5 (5a-6) GCF Cannot do
  - - - -3x²-15x+9= 3(x²+5x-3)
        
        6x²y-21x³y²+3x²y³ = 3x²y (2-7xy+y²)
- - - - a2 - b2 = (a+b) (a-b)
    - - x2 - 64 = (x-8) (x+8)
      - 36j2 - 49m2 = (6j-7m) (6j+7m)
      - 1/4x6 - 9/25x4 = (1/2x3-3/5x2) (1/2x3+3/5x2)
      - (x8 - 16) = (x4-4) (x4+4) = (x4-4) (x2+2) (x2+2)
  - - - How to Factor: a³+b³= (a-b)(a²+ab+b²)
        
        Exercises: x³+8=(x+2)(x²-2x+4) 27x4+8x7=x4(27+8x³)(4+6x+4x²)
      - Characteristics: Two Terms, both terms are perfect cubes, sum or difference
- - - - How to factor: (AC Method) You need to multiply A x C and then find 2 numbers that give the same as the result of the multiplication as AC like in this examples
        
        3x² -10x -8 (24)= 3x² -12x +2x -8 = 3x(x-4)2(x-4) = (3x+2) (x-4)
        4x² -26x-48(-192)= 4x²-32x+6x-48= 4x(x-8)+6(x-8)=(x-8)(4x+6)
  - - - Look for 2 numbers that multiplied give "c" and added or substrackted is "b", Trinomial (in descending order) Coefficient x² is 1
      - Examples
        
        x2+7x+12= (x+3)(x+4)
        
        m2+10m+21= (m+3)(m+4)