Unit 3

There are really only 2 main ideas in Unit 3:
(1) Finding ALL roots (solutions) of any polynomial, no matter how many. We've started this (see below).
(2) Graphing polynomial functions, and describing the graphs in certain mathematical ways. We'll get to this.

For finding the roots, you must be able to:

[1] Use the Rational Root Theorem to list all the POSSIBLE roots that are either whole numbers or simple fractions (so, without square roots or i's).

[2] Use the graphing calculator ([y=], [graph], and [2nd][graph] for the table) to figure out which of the POSSIBLE whole number roots actually ARE roots.

[3] Use Synthetic Division (from Unit 2) to divide the original long polynomial by the roots you know, to reduce it down to a quadratic.

[4] Solve the quadratic that's left, using factoring or the Quadratic Formula (we learned how to do this in Unit 1).

[*] Putting all those steps together, we can take a polynomial with 3, 4, or even more roots, and get ALL of the roots.

[*] Here are some additional examples of synthetic division, that we did in support Monday/Tuesday.

This might help for the Unit 2 test ...

Reference Flow Chart for Polynomial Identities:

Answer Key for the Review Pages (PURPLE - my 4A and 4B test will look similar to this) :
PART 1

PART 2

PART 3

PART 4

Answer Key for the Review Pages (YELLOW -Ms. Meade/Ms. Talley's test will look similar to this):
PART 1

 PART 2

 PART 3

 PART 4

Composition and Inverses - last new stuff for the test.

Notes from Thursday and Friday (10/8 and 10/9):

Review examples for test

The test is coming up next week (Thursday or Friday).

Here are some example problems:

 

 

 

Polynomial DIVISION

We have two methods for dividing polynomials:

(1) Long division. Long (like the name), takes time, and is kind of hard. But it's the ONLY method that works if you are dividing by ax+b, where a is ANYTHING besides =1.

Long division is shown on the left examples in the picture here.

(2) Synthetic division. Shorter, most people seem to find it easier. But it ONLY works if a=1 (dividing by x+b or x-b).

Synthetic division is shown on the right examples in the picture here. (click to enlarge)

Long Division Steps: 

1. Does                           Divide
2. McDonalds                 Multiply
3. Sell                             Subtract
4. Cheese                       Compare/check
5. Burgers?                     Bring down      then  Go back to step 1.

Synthetic Division Steps:  Bring Down 1st number.  Multiply, Add.  Multiply,Add; until done.