Problem: Find all the real zeros of the polynomial. Use the quadratic formula if necessary.



P(x)= x^3 + 4x^2 + 3x -2





To get the possible zeros of the polynomials p/q can help us, where p= 2

it is the last term. q = 1, this is the coefficient of the first term



We will factor p and q

p = 1*2 and -1*-2

  = 1, 2, -1, -2



q = 1*1 and -1*-1

  = 1, -1





possible zeros p/q are 1, -1, 2, -2



Test using synthetic division which among them are the real zeros of the polynomial



1   |   1    4     3    -2

             1     5     8

    _______________________

        1    5     8    6    --- > not a real zero





-1  |   1   4    3    -2

           -1   -3     0

    _____________________

        1   3    0    -2    ==> Not a real zero





2  |   1    4    3    -2

            2    12   30

   _____________________

       1    6    15   28   ====> not a real zero





-2    |  1   4   3   -2

            -2  -4    2

      _________________

         1   2  -1   0    ===> a Real zero



the factor now is (x + 2) (x^2 + 2x - 1)

                              |

                               --> we can use quadratic formula to get the factor for this where a = 1, b = 2 and c = -2



              



                  

               

                  



             



                       



               



               



There are 3 real zeros of the polynomial



   x= -2, 



   , 



     









Rmromero 

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