1. Essential Question: How do I use synthetic division to find all of the zeros?
What is synthetic division?
How do I find all the solutions given 1 root?

2. Is there another way to divide…of course!
Synthetic
Division

3. Use Synthetic Division to divide
x4 – 10x2 – 2x by (x + 3) -3 1
-10 -2 4 -3 9 3 -3 1 -3 -1 1 1
remainder

4. Practice Problem

5. You Try!!

6. Factors vs. Roots (Zeros)
Factors: What multiplies together to get the polynomial. The things in ( )
ex., (x+2), (2x-3), (x-8)
Roots: What the x values equal. After setting the factor =0. Can also be called zeros, or solutions.
ex., x=-2, x=3/2, x=8

7. Factor Theorem
If remainder = 0 when we plug a #, root, into some function, then (x – #) is a factor.

8. Before…
We could get a remainder using long division or synthetic division
The last number using synthetic division is your remainder!
We want a remainder of 0 to find the other roots…and we want to be able to find other roots!

9. Chapters 1 & 2 The Conservative Tradition in Educational Thought
Determine whether (x + 2) is a factor of f(x) = 3x3 - x2 + 2x - 4 NO
Answer:

10. You Try!! Determine whether (x - 6) is a factor of
f(x) = x4 - 6x3 - 4x + 24

11. Can you use synthetic division when you divide by 3x-2?

12. Let’s Put It All Together!!

13. Chapters 1 & 2 The Conservative Tradition in Educational Thought
If (x-1) is a factor, find the other factors of g(x) = 3x3 + 8x2 – 3x – 8 1 3 8 -3 -8 3 11 8 3 11 8
3x2
+11x +8
FACTOR using Kickback!
FACTORS:

14. You Try!! Given that (x-10) is a factor of , find the other factors.
What are the roots(zeros)?