& AM3.1d To Use The Rational Roots Theorem & Synthetic Division

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Presentation transcript:

10-19-18 & 10-22-18 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?

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

Active Learning Assignment Questions?

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.

ü (continued) Possible roots We will use these until we find a remainder of 0. Why? 1 2 1 -7 -6 -1 2 1 -7 -6 2 3 -4 -2 1 6 ü 2 3 -4 -10 2 -1 -6 (a) (b) (c) Now, what do we do?

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

What if some of you got 2 instead? Here is an arithmetic analogy: 2 1 -7 -6 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

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) 2 1 0 1 -1 2 1 0 1 2 3 3 -2 1 -1 ü 2 3 3 4 2 -1 1 (a) (b) (c) Now?...

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

ü Try: To save time, I will tell you what the one that works is: 4 9 22 5 -1 -2 -5 ü 4 8 20 (a) (b) (c) Now?...

(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:

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: #2 , #3, #6 , #7 (Even answers in are in brackets, Odd answers are in the back of the book.) WOW: Be the first to say “Hello”, say “Please” and “Thank you” a lot.