1a)    Solve the quadratic equation:   

                SOLUTION:      Of course the easiest way to solve a quadratic equation is to factor it. 

                                             But how do you factor a trinomial with numbers like this? 

                                   Find two numbers whose product is 640, so that if you take 3 times one of the factors and subtract the other factor you get 56.  Lots of luck doing that!! 

                                   Of course, if you have a graphing calculator you can use a program on the TI83+ or TI84 called “Polysmlt”, or with any graphing calculator, you can sketch the graph of   and find the zeros (or x-intercepts) of this graph.  These will be the solutions to the equation. 

                                   Using algebra techniques, you could always solve using the quadratic formula.

                                      , where

Notice that  just happens to be a perfect square (get out your calculator if you don’t already have it out!!) since .  Since this number within the radical is a perfect square, it means that the original problem could have been solved by factoring.  However, go ahead and finish the quadratic solution:

      or    

                    or   

                      or      

Now that you know what the solution is (a little “inside” information), could you actually solve the problem by factoring?  Let’s try again from the top:

       .

                  It does factor: 

                                   The factoring checks, and the solution is the same as with the quadratic formula.

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