Division of Polynomials

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					Division of Polynomials

    Homework Solutions
    Feb 19th Assignment
Long division
                                                       3
                          x2 –  7x + 2 +
                                                      x3
1.) x + 3            x3 – 4x2 – 19x + 9
                     x3 + 3x2           (change signs)
                         - 7x2 – 19x
                         - 7x2 – 21 x (change signs)
                                  2x + 9
                                  2x + 6 (change signs)
                                       3
Synthetic Division        -3     1    -4   -19   9
                                      -3   21    -6
                                 1    -7    2    3          x2 – 7x + 2 +
                                 x2   x    #     R
Long division – ADD in the 0x2 term
                  4x2 + 28x - 4
2.) x - 7 4x3 + 0x2 – 200x + 28
           4x3 - 28x2          (change signs)
               + 28x2 – 200x
               + 28x2 – 196x (change signs)
                        -4x + 28
                        -4x + 28 (change signs)
                              0
Synthetic Division   7   4        0       -200   28
                                  28      196    -28
                         4        28       -4    0     4x2 + 28x - 4
                             x2       x     #    R
Long division
                                            19
                  5x + 4 +                 2x  3

3.) 2x - 3 10x2 – 9x + 7
           10x2 – 15x                         (change signs)
                   8x + 7
                   8x – 12                   (change signs)
                        19


Cannot do synthetic division with this problem.
Long division
                          4x2 – 1x - 5 - 2 x5 3
4.) 2x + 3         8x3 + 10x2 – 13x - 20
                   8x3 + 12x2             (change signs)
                         -2x2 – 13x
                         -2x2 – 3x (change signs)
                              -10x - 20
                              -10x - 15 (change signs)
                                      -5
Synthetic Division cannot be done with this problem
Long division ADD in 0x2 and 0x terms!!!
                  x2 + 9x + 81
5.) x - 9 x3 + 0x2 + 0x - 729
           x3 - 9x2            (change signs)
                9x2 + 0x
                9x2 – 81x (change signs)
                      81x - 729
                      81x - 729 (change signs)
                              0
Synthetic Division   9   1    0   0    729
                              9 81 -729
                         1    9   81    0    x2 + 9x + 81
                         x2   x   #     R
Long division
                        x2 – 3x + 2
6.) x - 4        x3 – 7x2 + 14x - 8
                 x3 - 4x2             (change signs)
                     - 3x2 + 14x
                     - 3x2 + 12x (change signs)
                               2x - 8
                               2x - 8 (change signs)
                                    0
Synthetic Division     4   1    -7   14    -8
                                4    -12   8
                           1    -3    2     0   x2 – 3x + 2
                           x2   x     #     R
Long division
                                                       2
                          x2 –   4x + 5 +             x2
7.) x + 2            x3 – 2x2 – 3x + 12
                     x3 + 2x2            (change signs)
                         - 4x2 - 3x
                         - 4x2 – 8x (change signs)
                                5x + 12
                               5x + 10 (change signs)
                                      -1
Synthetic Division        -2     1    -2   -3   12
                                      -2   8    -10
                                 1    -4    5     2     x2 – 4x + 5 +
                                 x2   x    #     R
Long division                        25
                           x+ 2 -   x4
8.) x + 4            x2 + 6x - 17
                     x2 + 4x          (change signs)
                         2x – 17
                         2x + 8 (change signs)
                              -25


Synthetic Division        -4    1   6     -17
                                    -4    -8
                                1   2      -25   x+2-
                                x   #      R
Long division
                                             26
                            2x + 6 +        3x  5
9.) 3x - 5           6x2 + 8x - 4
                     6x2 - 10x         (change signs)
                           18x – 4
                           18x - 30 (change signs)
                                 26


Synthetic Division        cannot be done with this problem
Long division
                              x2 + 3x + 5
10.) x - 6           x3 - 3x2 – 23x + 30
                     x3 - 6x2           (change signs)
                          3x2 – 23x
                          3x2 – 18x    (change signs)
                                  5x + 30
                                  5x - 30 (change signs)
                                        0
Synthetic Division       6    1   -3   -23   30
                                  6    18 -30
                              1 3      5     0    x2 + 3x + 5
                              x2 x     #     R

				
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