• Factoring By Extracting (GCF)

    This is always the first type of factoring that you should try.  It is the easiest and the fastest to use.  What you do is in an expression or equation find the greatest common factor and factor it to the outside of a set of parentheses.  On the inside of the parentheses you will write what is remaining after you factor the term away.   Look, this is actually the distributive property working backwards!!!
    example:    
      2x2 - 8x
      2x(x - 4)
     
    GCF is 2x 
    check by distributing
    example:
      4a + 8ab - 12ac
      4a(1 + 2b - 3c)
    example:
      5x2 + 15x = 0
      5x(x + 3) = 0
      x = 0 or -3
     
    If you have an equation, make sure one side is equal to zero.
    solve using zero product property.
    example:
    A man falls over Niagara Falls in a barrel that follows the path of  h=300t-15t2.  After how many seconds will he reach the bottom of the falls?  (h=height, t=time in seconds)
    We need to decide what height we are looking for first.  The bottom of the falls should have a height of 0.  So we need to solve  300t-15t²=0
    300t-15t²=0  factor
    15t(20-t)=0  solve
    15t=0 or 20-t=0
    t= 0 or 20
    Now in this case t can't be equal to 0. That's before they went over the falls so t must be equal to 20 seconds.  (Think about practical situations and what kind of answers they can have.)