Factoring Flow Chart   (What Do I Do?) 
                                                                                                                                                                                                                                                                                                              REMEMBER: 
                                                                                                                                                Question #1:                                                                                                                                                   
                                                                                                                 Is there a Greatest Common Factor?                                                                                                                                                            = 0 means to SOLVE!   
                                                                                                                                                      (GCF?)                                                                                                                                                   
                                                                                                                                                                          No                                                                                                                                  If the polynomial is set equal 
                                                                                                  Yes                                                                                                                                                                                                         to 0, factor first and then set 
                                                                                                                                                                                                                                                                                                              both factors equal to 0 and 
                                                                                                                                                                                                                                                                                                              solve.   
             Factor out the GCF                                                                                                 Question #2:  Does it have four terms? 
              
             Answer:  Product of a                                                                                      Yes                                                            No                                                          Question #3:  Is it a trinomial? 
             monomial and a polynomial. 
              
                               GCF (Leftovers) 
                                                                                                                                       Box Method                                                                                                     Yes                                          No                                      Question #4:   
                                                                                                                                                                                                                                                                                                                                           Is it a binomial? 
                                                                                                                                       Write one term in each box and 
             Look at the leftovers and go back through                                                                                 factor. 
             the chart to see if they can be factored                                                                                                                                                                                                         Question #5:                                                     Yes                                             No 
             more!                                                                                                                     Answer:  Product of two binomials.                                                                                     Is it a difference  
                                                                                                                                                                                                                                                              of squares? 
              X-Box Method 
               
              Write the first term of the trinomial in the upper left hand box                                                                                                                                                                                                                                        Question #6:  Is it a sum 
              and the last term in lower right hand box.                                                                                                                                                                         Yes                                           No                                     or difference of cubes? 
               
                   LOOK FOR TWO SPECIAL NUMBERS THAT: 
               
                                                                                                              a        c                                             2
                                Multiply to:  a                         c                                                                                   ax  
                                                                     
                                      Add to:  b                                                                                                                                                                         Use the pattern:                                                                  Yes                                                         No 
                                                                                                                                                                                                                            2         2
                                         2                                                                        b                                                                                                      a  – b  = (a – b) (a + b) 
                                 ax  + bx + c                                                                                                                                  c 
               
                                                                                                                                                                                                                         Use one of the patterns: 
              Write your new terms in the upper right hand box and the lower left hand box.                                                                                                                                 3          3                            2                    2
                                                                                                                                                                                                                         a  + b  = (a + b) (a  – ab + b ) 
                                                                                                                                                                                                                            3         3                           2                    2                                If you can’t find anything 
              FACTOR!                                                                                                                                                                                                    a  – b  = (a – b) (a  + ab + b ) 
                                                                                                                                                                                                                                                                                                                        that works, it might not 
                                                                                                                                                                                                                          
              Answer:  Product of two binomials.                                                                                                                                                                                                                                                                        be factorable.   
                                                                                                                                                                                                                                                                                                                        In that case, it is PRIME!