3x 2 6x3 5x2 12x 4

1
D M S B
2x2
3x
2
3x 2 6x3 - 5x2 12x 4
6x3
4x2
-9x2
12x
-9x2
6x
6x
4
6x
4
0
Check
(3x 2)(2x2 3x 2)
6x3 9x2 6x 4x2 6x 4
6x3 5x2 12x 4
2
7 (2x 1)
2x2
3x
1

2x 1 4x3 8x2 5x 8
4x3 2x2
-6x2 5x
-6x2 3x
2x 8
2x 1
remainder
- 7
Check
(2x 1)(2x2 3x 1)
4x3 6x2 2x 2x2 3x 1
4x3 8x2 5x 1
Add remainder -7
4x3 8x2 5x 8
3
3x
1
5x2
5x4 15x3
3x3
10x2
3x
x2
x2 3x
0
4
Factor
5x4 18x3 10x2 3x
Divide to find that the other factor is
5
Synthetic Division
(3x3 8x2 5x 7) ? (x 2)
3
8
5
-7
-2
-6
-4
-2
3
2
1
-9
remainder
9 x 2


x2
x
answer
6
Synthetic Division
(2x4 6x3 x2 3x 3) ? (x 3)
2
-6
1
-3
-3
3
6
0
0
3
-3
2
0
1
0
remainder
2x3
answer
0x2 1x 0
3 (x 3)
2x3 x
7
Synthetic Division
(x4 2x3 70x 20) ? (x 5)
1
-2
0
-70
20
5
5
25
15
75
45
1
3
15
5
remainder
45 (x 5)
answer
x3 3x2 15x 5
8
Synthetic Division
(4x3 8x2 3x 8) ? (2x 1)
3 2
2
-4
-4
-3 2
1
0
-4
2
-3
0
remainder
4 (2x 1)
answer
2x2 3x
9
Synthetic Division
( 6x2 x 7) ? (3x 1)
2
2
-1
-2
remainder
answer
2 (3x 1)
2x 1