Unit 8

Polynomials and Factoring

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Equivalence
Essential Question: Can two algebraic expressions that appear to be different be equivalent?

Properties
Essential Question: How are the properties of real numbers related to polynomials?
   

 

Desmos.com Graphing Calculator

Shodor.com Graphing Calculator

 

Lesson/Objective Supplemental Lessons On-line Practice Suggested
Homework
8-1  Polynomials and Factoring

Objective:  To solve systems of equations by graphing. To analyze special systems.

Essential Understandings: 
Monomials can be combined to form larger expressions called polynomials. Polynomials can be simplified using addintion and subtraction.
 


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Classifying Polynomials using the DEGREE and number of terms

Adding Polynomials

Subtracting Polynomials


self-check quiz

Solve It!

Additional
PROBLEMS

Enrich!

hw#8-1: Due 

Read pg 474-477
#1-15 All
#17,21,25,32,35,38,42,45,47,52,66

Know you new vocabulary:
Monomial; Polynomial; Degree of a monomial; Degree of a polynomial; Degree of a term

Re-read and understand COMBINING LIKE TERMS

New Learning
- Standard Form of a Polynomial
- Add & Subtract Polynomials Vertically & Horizontally
8-2  Multiplying and Factoring

Objective:  To multiply a monomial by a polynomial 

Multiplying with Algebra Tiles

Essential Understandings: You can use the DISTRIBUTIVE PROPERTY to multiply a  monomial by a polynomial using various techniques including area models and algebra tiles
 


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Multiplying and Factoring

Multiplying Polynomials including the FOIL Method


self-check quiz

Solve It!

Additional
PROBLEMS

Enrich!
 

hw#8-2: Due

pg 483 #9-33 Odd, 36-39 All
8-3  Multiplying Binomials

Objective:  To multiply two binomials or a binomial by a trinomial

Essential Understandings: There are several ways to find the product of two binomials, including distribution, models, tables, and algebra tiles
 


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Multiplying Polynomials including the FOIL Method


self-check quiz

Solve It!

Additional
PROBLEMS

Enrich!
 

hw#8-3: Due 

pg 501-502 #9-43 EVERY OTHER ODD (ff course, you can do all of the ODDS for extra practice)

 

hw#8-4: Due 

pg 507-508 #9-16 All, 17, 25-30 Odd, 37-43 Odd, 49

USE BOTH FOIL AND the AREA MODEL
(the book discusses the "distribution" and a table method, both are very similar to what we have done in class, so just use any method you are comfortable with)

Observing the Multiplication of Polynomials

8-4  Multiplying Special Cases

Objective: To find the products and recognize patterns in the multiplication of special cases of binomials

Essential Understandings: 
There are special rules that govern the multiplication of certain instances of binomial terms. These rules generate patterns that will be helpful in future work 
 

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Special Cases including "difference of squares"


 


self-check quiz

Solve It!

Additional
PROBLEMS

Enrich!

 

8-5  Factoring
        x2 + bx + c

Objective: To factor "simple" quadratic trinomials

Essential Understandings: 
You can write some trinomials of the form x2+bx+c as the product of two binomials
 

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Factoring EASY trinomials
 

 

YOU SHOULD FOCUS YOUR EFFORTS ON 8-1 thru 8-4 since that is what is on the quiz... a good idea would be to do some problems on the Mid-Chapter Quiz on page 510...

hw#8-5: Due 

(don't worry too much about this assignment... we will be reviewing it next week)
pg 514 #1-9 All, #11,15,23,27,31,35 (#35 is a little tricky... see Problem 5 on pg 514)
pg 520-521 #15,19,23

UNIT 8 QUIZ on Sections 8-1 thru 8-4 
TBA

8-6  Factoring
        ax2 + bx + c

Objective: To factor quadratic trinomials with a leading coefficient <> 1

Essential Understandings: 
You can write some trinomials of the form ax2+bx+c as the product of two binomials

 

 


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Factoring HARD Quadratics
 

 

  hw#8-6: Due 

pg 508-09
#1-5 All
#15-25 Odd

Complete
Problem Set 8A

... look at Problem Set 8B ... for our review on 

For your reference:
Observing the Multiplication of Polynomials

 

8-7  Factoring Special Cases

 

HINT from Mr. C.
"SPECIAL" Cases are nothing special... they follow ALL the same rules that you have learned with the AREA MODEL (aka the BOX).
  hw#8-7 Due 

pg 523-527
Chapter 8 Review & Chapter Test
#1 - Infinity... this means that you should review EVERYTHING in the Review section... do every third or fourth problem to make sure you are on target for the test... when in doubt, the AREA MODEL and the SYMMETRY OF THE BOX will always save you!!

 

8-8  Factoring by Grouping

 


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Factoring by Grouping

  OPTIONAL - NOT ON UNIT TEST
UNIT TEST REVIEW   UNIT 8 EXTRA PRACTICE

CUMULATIVE REVIEW 1-8

 
UNIT 8 TEST
(you will not be responsible for the factoring by grouping technique shown in section 8-8)
TBA