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Find the quotient and remainder using long division for

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2 Answers

Synthetic division:

4 |  1     -6     13     -28

              4     -8       20

       1    -2      5       -8

x^2   -2x    +5    -8/(x-4)

Using polynomial long division we get

                   x2  -  2x  +  5

         _________________

x - 4  |  x3 - 6x2 + 13x - 28

            x3 - 4x2                  = x2(x - 4)

           ----------

                 -2x2 + 13x

                 -2x2 +   8x        = -2x(x - 4)

                  -------------

                            5x - 28

                            5x - 20  = 5(x - 4)

                           ----------

                                   -8

Thus the quotient is x2 - 2x + 5. The remainder is -8, just as you said.

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