# Division of Polynomials by yurtgc548

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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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