1. Dividing Polynomials WOW! I want to learn how to do that?
Why would you want to do that?
What do you find when
you divide 15 by 5?
What do you find when you
divide ( 6x3 – 5x2 – 12x – 4 )
by (3x+2)?
You find 3, the other
factor of 15
You find 2x2 – 3x – 2, another
factor of the polynomial.
Which you can then factor
into (2x+1)(x-2)

2. 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

3. 2x – 1 4x3 – 8x2 + 5x – 8 2x2 – 3x + 1 4x3 – 2x2 + 5x -6x2 -6x2 + 3x7
(2x – 1)
2x – x3 – 8x2 + 5x – 8
4x3 – 2x2
+ 5x
-6x2
-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

4. x2 + 3x 5x4 + 18x3 + 8x2 – 3x 5x2 + 3x – 1 5x4 + 15x3 3x3 + 8x2 3x3

6. Synthetic Division:
Your divisor must be x - #
Who’s in the house? ┘
Write the coefficients using zeros if needed.
Drop it like it’s hot! (one time)
Multiply by the house, then add. (repeat)

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

8. (3x4 + 13x3 + 2x2 - 3x + 20)  (x + 4) -4 3 13 2 -3 20 -12 -4 8 -20 3
Synthetic Division
(3x4 + 13x3 + 2x2 - 3x + 20)  (x + 4) -4 3 13 2 -3 20
-12 -4 8
-20 3 1 -2 5
remainder
answer 1 3
- 2 5 x3
+ x2 x +

9. 2 6
-18
-120
120 12 24 48 60 6 12 24 30 60

10. Synthetic Division (x4 – 5x2 – 36)  (x – 3) 3 1 -5 -36 3 9 12 36 1 3-5
-36 3 9 12 36
remainder 1 3 4 12
answer
x3 + 3x2 + 4x + 12
 (x + 3) -3 1 3 4 12 -3
-12
Imaginary
factors 1 4
x2 + 4

11. Synthetic Division
(3x3 – 13x2 – 7x + 2)  (3x + 2) 2 3
-13 3
- 7 3 2 3 1 10 3
- 2 3 -2 3 1 -5 1
remainder
answer
x2 – 5x + 1

12. (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 –

13. 5x4 + 18x3 + 8x2 - 3x 5x2 + 3x – 1 Factor: One factor is x2 + 3x
Divide to find that the other factor is:
5x2
+ 3x
– 1
Connection: the solutions to 5x4 + 18x3 + 8x2 - 3x = 0
are …
x = 0 and x = -3 and =
x = = .24 and x = = -.84

14. ( 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 –