Find the quotient and remainder using long division for

Question

Find the quotient and remainder using long division for
\frac(x^3 -6 x^2 + 13 x -28)(x-4)

The quotient is ?
The remainder is  -8

Answer 1

Synthetic division:

4 |  1     -6     13     -28

              4     -8       20

       1    -2      5       -8

x^2   -2x    +5    -8/(x-4)

Answer 2

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.