1.
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AM3.1d To Use The Rational Roots Theorem & Synthetic Division
Please have your notebook out and ready to go, we have lots to do!
Got ID?

2. Opener:
For each, find all possible factors and how many:
Number: Factors: How many:
Try: 2 -7 9 12
-15
-24

3. Active Learning Assignment Questions?

4. LESSON: To solve:
(Leading Coeffcient)
(Constant term)
1. Find all possible factors of -6:
2. Find all possible factors of 2:
3. Find all possible combinations of
Thus, these are all the possible rational roots that you will try with synthetic division to get the zeros.

5. ü (continued) Possible roots
We will use these until we find a remainder of 0. Why? 1 -1 2 3 -4 -2 1 6 ü 2 3 -4
-10 2 -1 -6
(a)
(b)
(c)
Now, what do we do?

6. Factor by sight:
Or use the Quadratic Formula
Thus, the zeros of the polynomial are:

7. What if some of you got 2 instead? Here is an arithmetic analogy:
What if some of you got 2 instead? 4 10 6 ü
Here is an arithmetic analogy: 2 5 3 30 30 30 2 15 3 10 5 6 3 5 2 5 2 3

8. ü Try: Possible: 1 2 1 0 1 -1 2 1 0 1 2 3 3 -2 1 -1 2 3 3 4 2 -1 1 (a) -1 2 3 3 -2 1 -1 ü 2 3 3 4 2 -1 1
(a)
(b)
(c)
Now?...

9. (continued)
Use the Quadratic Formula
Thus, the zeros of the polynomial are:

10. ü Try: To save time, I will tell you what the one that works is: -1 -2 -5 ü 4 8 20
(a)
(b)
(c)
Now?...

11. (continued)
Use the Quadratic Formula
(Helpful Hint:)
(Can be reduced. Divide both sides by 4. You will get the same answer either way.)
Thus, the zeros of the polynomial are:

12. Active Learning Assignment:
P. 82 Copy the Rational Roots Theorem. Put it on a separate sheet, with your name on it. It will be turned in, next time that you come in.
P. 83: # , #3, # , #7
(Even answers in are in brackets, Odd answers are in the back of the book.)
WOW:
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