1. 3x + 2 6x3 - 5x2 – 12x – 4 2x2 – 3x – 2 6x3 + 4x2 -9x2 – 12x -9x2 – 6xD M S B
3x x3 - 5x2 – 12x – 4
6x3
+ 4x2
-9x2
– 12x
-9x2
– 6x
– 6x
– 4
– 6x
– 4
Check:
(3x + 2)(2x2 – 3x – 2)
= 6x3 – 9x2 – 6x + 4x2 – 6x – 4
6x3 – 5x2 – 12x – 4

2. 2x – 1 4x3 – 8x2 + 5x – 8 2x2 – 3x + 1 4x3 – 2x2 -6x2 + 5x -6x2 + 3x7
(2x – 1)
+ 1 –
2x – x3 – 8x2 + 5x – 8
4x3 – 2x2
-6x2 + 5x
-6x2 + 3x
2x – 8
2x – 1
- 7
remainder
Check:
(2x – 1)(2x2 – 3x + 1)
= 4x3 – 6x2 + 2x – 2x2 + 3x – 1
= 4x3 – 8x2 + 5x – 1
Add remainder -7
= 4x3 – 8x2 + 5x – 8

3. x2 + 3x 5x4 + 18x3 + 10x2 +3x 5x2 + 3x + 1 5x4 + 15x3 3x3 + 10x2 3x3

4. 5x4 + 18x3 + 10x2 +3x 5x2 + 3x + 1 Factor: One factor is x2 + 3x
Divide to find that the other factor is:
5x2
+ 3x
+ 1

5. 2 3 1 (3x3 + 8x2 + 5x – 7)  (x + 2) -2 3 8 5 -7 -6 -4 -2 3 2 1 -9 –
Synthetic Division
(3x3 + 8x2 + 5x – 7)  (x + 2) -2 3 8 5 -7 -6 -4 -2 3 2 1 -9
remainder 9
x + 2 2 3 1 –
answer x2
+ x +

6. (2x4 – 6x3 + x2 – 3x – 3)  (x – 3) 3 2 -6 1 -3 -3 6 3 2 1 -3 2x3
Synthetic Division
(2x4 – 6x3 + x2 – 3x – 3)  (x – 3) 3 2 -6 1 -3 -3 6 3 2 1 -3
remainder
answer
2x3
+ 0x2 + 1x + 0 3
(x – 3)
2x3 + x –

7. Synthetic Division
(x4 – 2x3 – 70x + 20)  (x – 5) 5 1 -2
-70 20 5 15 75 25 1 3 15 5 45
remainder 45
(x – 5)
answer
x3 + 3x2 + 15x + 5 +

8. (4x3 – 8x2 + 3x – 8)  (2x – 1) 2 -4 -4 1 2 -3 -4 2x2 – 3x –
Synthetic Division
(4x3 – 8x2 + 3x – 8)  (2x – 1) 1 2 3 2 2 -4 -4 -3 2 1 2 -3 -4
remainder 4
(2x – 1)
answer
2x2 – 3x –

9. ( 6x2 – x – 7)  (3x + 1) 2 2 -1 -2 2x – 1 – Synthetic Division 1 3 2-7 3 2 -2 3 1 3 2 -1 -2
remainder
answer 2
(3x + 1)
2x – 1 –