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The polynomial p(x) = 3x^3 - 20x^2+ kx + 12 is divisible by x - 3 for some constant k. Factor p(x) completely.

 Aug 8, 2021
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x-3      when x = 3 is subbed into the equation Remainder = 0 `

 

  so   k = 29

 

         ________3x^2 -11x_-4___________

  x-3|   3x^3 - 20x^2+29x+12

            3x^3   -9x^2

                      -11x^2 + 29 x +12

                      -11x^2  +33x

                                  - 4x  + 12

                                  -4x   +12                   

                                                    R = 0

 

Now factor   3x^2 - 11x -4          (3x+1)(x-4)      then don't forget the RED factor above:

                                p(x) =   (x-3)(3x+1)(x-4)  

 Aug 8, 2021

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