2. 3x + 2 6x 3 - 5x 2 – 12x – 4 DMSBDMSB 2x 2 6x 3 + 4x 2 -9x 2 – 12x – 3x -9x 2 – 6x – 4 – 2 – 6x– 4 0 Check: (3x + 2)(2x 2 – 3x – 2) = 6x 3 – 9x 2 – 6x + 4x 2 – 6x – 4 6x 3 – 5x 2 – 12x – 4

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

4. x 2 + 3x 5x 4 + 18x 3 + 10x 2 +3x 5x 2 5x 4 + 15x 3 3x 3 + 10x 2 + 3x 3x 3 + 9x 2 x2x2 + 3x + 1 x 2 + 3x 0

5. 5x 4 + 18x 3 + 10x 2 +3x Factor: One factor is x 2 + 3x Divide to find that the other factor is: 5x 2 + 3x+ 1

6. Synthetic Division (3x 3 + 8x 2 + 5x – 7)  (x + 2) -2 385-7 3 -6 2 -4 1 -2 -9 remainder answer x2x2 231 + x + – 9 x + 2

7. Synthetic Division (2x 4 – 6x 3 + x 2 – 3x – 3)  (x – 3) 3 2-61-3 2 6 0 0 1 3 0 remainder answer -3 0 2x 3 + 0x 2 + 1x + 0 2x 3 + x – 3 (x – 3)

8. Synthetic Division (x 4 – 2x 3 – 70x + 20)  (x – 5) 5 1-20-70 1 5 3 15 75 5 remainder answer 20 25 45 x 3 + 3x 2 + 15x + 5 + 45 (x – 5)

9. Synthetic Division (4x 3 – 8x 2 + 3x – 8)  (2x – 1) 2-4 3232 2 1 -3 2 0 0 -4 remainder answer 2x 2 – 3x – 4 (2x – 1) 1212

10. Synthetic Division ( 6x 2 – x – 7)  (3x + 1) 2 2 -2 remainder answer 2x – 1 – 2 (3x + 1) 1313 3 -7 3 -2 3 1313