1. Polynomials
November 28 Tuesday

2. Tuesday 28 November Warm up
Common Board
Standard:
A- APR.1.1 –understand polynomials are closed under certain operations
F-IF.3.7- describe end behavior of polynomials
Learning Goal: Classify polynomials
Determine end behavior
Describe the shape of polynomials
EQ: What do you have to do before classifying each polynomial?
What does the degree of a polynomial tell you about the graph?
Agenda:
Warm up
Notes
Practice together
Practice on your own (finish for HW if necessary.
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree
Tuesday 28 November Warm up

3. Common Board
Standard:
A- APR.1.1 –understand polynomials are closed under certain operations
F-IF.3.7- describe end behavior of polynomials
Learning Goal: Classify polynomials
Determine end behavior
Describe the shape of polynomials
EQ: What do you have to do before classifying each polynomial?
What does the degree of a polynomial tell you about the graph?
Agenda:
Warm up
Notes
Practice together
Practice on your own (finish for HW if necessary.
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree
Monomial – a number , variable or product of number and variable. *** monomials can not have variables in the denominator – variables with negative exponents- variables under radical signs EXAMPLES: Monomial- 2 , x , 4𝑥 2 , 𝑎 3 𝑏 2 c Not monomial- 𝑥 −1 , 𝑥 , x + 4 constant - a monomial with NO variable ex: 7 coefficient - the numerical factor of a monomial ex: 2x 2 is the coefficient degree – sum of the variables exponents ex: 7𝑎 2 𝑏 3 𝑐 degree is 6

4. Common Board
Standard:
A- APR.1.1 –understand polynomials are closed under certain operations
F-IF.3.7- describe end behavior of polynomials
Learning Goal: Classify polynomials
Determine end behavior
Describe the shape of polynomials
EQ: What do you have to do before classifying each polynomial?
What does the degree of a polynomial tell you about the graph?
Agenda:
Warm up
Notes
Practice together
Practice on your own (finish for HW if necessary.
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree
Polynomial – a monomial or a sum of monomials Terms - the monomials that make up a polynomials – separated by addition/subtraction Like terms – same variable – same exponent Degree of polynomial – the single term with the highest degree Standard form of polynomial – descending order of exponents (alphabetical if more than 1 variable) Leading term – the term with the greatest degree Leading Coefficient- the coefficient of the leading term Classify Polynomials - by degree and number of terms Degree Number of terms constant monomial 1 – linear binomial 2- quadratic trinomial 3 – cubic or more- polynomial 4- quartic 5- quintic

5. Common Board
Standard:
A- APR.1.1 –understand polynomials are closed under certain operations
F-IF.3.7- describe end behavior of polynomials
Learning Goal: Classify polynomials
Determine end behavior
Describe the shape of polynomials
EQ: What do you have to do before classifying each polynomial?
What does the degree of a polynomial tell you about the graph?
Agenda:
Warm up
Notes
Practice together
Practice on your own (finish for HW if necessary.
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree
Shape of Polynomials
End behavior – is determined by the leading coefficient and the degree Degree – even end behavior is either up – up or down down Degree odd end behavior is down – up or up- down Turning points - at most 1 less than the degree

6. Determine the degree when given a table or points
Make sure that the x values are in a constant pattern
Find the difference in the y values ( subtract) – if there is a constant difference in the y values then it is LINEAR ( constant rate of change)
Find the difference in the answers from step if there is a constant difference in this second step it is quadratic
Find the difference in the answers from step 3 - if there is a difference in this third step then this is cubic.
Continue until you find a constant change

8. Practice like the HW

9. Common Board
Standard:
A- APR.1.1 –understand polynomials are closed under certain operations
F-IF.3.7- describe end behavior of polynomials
Learning Goal: 1. Write polynomials in factored form
2. Find zeros 3. Write polynomials in standard form given zeros. 4. use multiplicity to describe behavior.
EQ: How can knowing the zeros of a polynomial help to describe the behavior of the polynomial?
Agenda:
Warm up
Notes and examples
Practice together
Practice on your own (finish for HW if necessary.
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree – factors- synthetic division- quadratic formula – zeros – multiplicity-
Wednesday 29 Nov Warm – up Determine the degree from the given table

10. LG- write polynomials in factored form process: look for a gcf factor or use quadratic formula factor by grouping use synthetic division Examples: − 2𝑥 𝑥 2 +56x 𝑥 𝑥 2 -8x 𝑥 4 +5𝑥 𝑥 2 −20𝑥 −12

11. Common Board
Standard:
A- APR.1.1 –understand polynomials are closed under certain operations
F-IF.3.7- describe end behavior of polynomials
Learning Goal: 1. Write polynomials in factored form
2. Find zeros 3. Write polynomials in standard form given zeros. 4. use multiplicity to describe behavior.
EQ: How can knowing the zeros of a polynomial help to describe the behavior of the polynomial?
Agenda:
Warm up
Notes and examples
Practice together
Practice on your own (finish for HW if necessary.
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree – factors- synthetic division- quadratic formula – zeros – multiplicity-
LG- Find the zeros when given factored form ( use zero product property) Process: set each factor = to 0 and solve Multiplicity is when a zero repeats if the multiplicity is even then the graph “bounces” off (turns around) at the x- axis if the multiplicity is 1 then it crosses like a line and if it is odd greater than 1 if behaves like a cubic function and crosses the x axis with a “hesitate” Examples: What are the zeros and name any multiplicities … y = (x+2)(x-1)(x-3) y = (x+2 ) 2 (x-2)(x-3)

12. Common Board
Standard:
A- APR.1.1 –understand polynomials are closed under certain operations
F-IF.3.7- describe end behavior of polynomials
Learning Goal: 1. Write polynomials in factored form
2. Find zeros 3. Write polynomials in standard form given zeros. 4. use multiplicity to describe behavior.
EQ: How can knowing the zeros of a polynomial help to describe the behavior of the polynomial?
Agenda:
Warm up
Notes and examples
Practice together
Practice on your own (finish for HW if necessary.
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree – factors- synthetic division- quadratic formula – zeros – multiplicity-
LG- Write polynomials in standard form if you are given the factored form – distribute and combine like terms if you are given the zeros – write as factors and then distribute and combine like terms examples: y = (x+2 ) 2 (x-2)(x-3) or zeros are -2, 2 and 3 HW – 1-24 ALL 31,32,34,35

13. Thursday November 30 Complete the warm – up paper Choose a partner to complete the matching activity 

14. Common Board
Standard:
A- REI.4.1 –explain why x intercepts are solutions
F-IF.3.7- describe end behavior of polynomials
N-CN.3.7 Solve quadratic equations with real coefficients that have complex solutions
Learning Goal: 1. Write polynomials in factored form
2. Find zeros 3. Write polynomials in standard form given zeros. 4. use multiplicity to describe behavior.5. DESCRIBE each theorem
EQ: What is the advantage of combining the rational roots theorem with synthetic division?
How can the Fundamental Theorem of Algebra help when solving polynomials?
Agenda:
Warm up –Powerpoint-Practice
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree – factors- synthetic division- quadratic formula – zeros – multiplicity-
Monday December 4 Grab a computer IF you are done with your polynomial poster Warm up – Given 𝑎 2 − 𝑏 𝑎 3 − 𝑏 𝑎 3 + 𝑏 3 LABEL a and b 4 𝑥 2 −25 𝑥 3 −8 64𝑥 𝑥 3 − 𝑥 3 −125𝑥

15. Polynomial Factoring Techniques- use the Fundamental Theorem of Algebra to mentally determine number of solutions by checking degree of the polynomial 1. take out a GCF 2. Look for perfect situations 𝑎 2 − 𝑏 USE (a +b)(a-b) 𝑎 2 +2𝑎𝑏+ 𝑏 2 USE (a+b ) 2 𝑎 2 −2𝑎𝑏+ 𝑏 2 USE (a-b ) 2 𝑎 3 − 𝑏 USE (𝑎−𝑏)( 𝑎 2 +ab+ 𝑏 2 ) 𝑎 3 + 𝑏 USE (𝑎+𝑏)( 𝑎 2 −𝑎𝑏+ 𝑏 2 ) 3. if degree greater than 2 use the rational roots theorem and synthetic division 4. WHEN quadratic – factor or factor by grouping or quadratic formula WRITE THE FACTORS and SOLUTIONS for the WARM UP a. Finish your polynomial poster then work with computer to get notes and complete your HW

16. Some Theorems ….. Rational Root Theorem EXAMPLE:
Common Board
Standard:
A- APR.1.1 –understand polynomials are closed under certain operations
F-IF.3.7- describe end behavior of polynomials
Learning Goal: 1. Write polynomials in factored form
2. Find zeros 3. Write polynomials in standard form given zeros. 4. use multiplicity to describe behavior.
EQ: How can knowing the zeros of a polynomial help to describe the behavior of the polynomial?
Agenda:
Warm up
Notes and examples
Practice together
Practice on your own (finish for HW if necessary.
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree – factors- synthetic division- quadratic formula – zeros – multiplicity-
Some Theorems ….. Rational Root Theorem EXAMPLE:

17. Common Board
Standard:
A- APR.1.1 –understand polynomials are closed under certain operations
F-IF.3.7- describe end behavior of polynomials
Learning Goal: 1. Write polynomials in factored form
2. Find zeros 3. Write polynomials in standard form given zeros. 4. use multiplicity to describe behavior.
EQ: How can knowing the zeros of a polynomial help to describe the behavior of the polynomial?
Agenda:
Warm up
Notes and examples
Practice together
Practice on your own (finish for HW if necessary.
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree – factors- synthetic division- quadratic formula – zeros – multiplicity-
You try the Rational Roots Theorem … 3𝑥 3 + 7𝑥 2 +6𝑥−8=0 more Theorems that we have already used … you try…. 𝑥 5 − 𝑥 4 − 3𝑥 3 + 3𝑥 2 −4𝑥+4

18. HW -Practice 1-16 in google classroom and on website
Common Board
Standard:
A- APR.1.1 –understand polynomials are closed under certain operations
F-IF.3.7- describe end behavior of polynomials
Learning Goal: 1. Write polynomials in factored form
2. Find zeros 3. Write polynomials in standard form given zeros. 4. use multiplicity to describe behavior.
EQ: How can knowing the zeros of a polynomial help to describe the behavior of the polynomial?
Agenda:
Warm up
Notes and examples
Practice together
Practice on your own (finish for HW if necessary.
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree – factors- synthetic division- quadratic formula – zeros – multiplicity-
HW -Practice 1-16 in google classroom and on website

19. Tuesday December 5 extra credit for the complete justified answer
Common Board
Standard:
A- APR.1.1 –understand polynomials are closed under certain operations
F-IF.3.7- describe end behavior of polynomials
Learning Goal: 1. Write polynomials in factored form
2. Find zeros 3. Write polynomials in standard form given zeros. 4. use multiplicity to describe behavior.
EQ: How can knowing the zeros of a polynomial help to describe the behavior of the polynomial?
Agenda:
Warm up
Notes and examples
Practice together
Practice on your own (finish for HW if necessary.
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree – factors- synthetic division- quadratic formula – zeros – multiplicity-
Tuesday December 5 extra credit for the complete justified answer

20. Descartes’ Rule

21. Wrap up extra credit for each justified complete answer

22. Binomial Theorem and Pascal’s Triangle (326)
Common Board
Standard:
A- APR.1.1 –understand polynomials are closed under certain operations
F-IF.3.7- describe end behavior of polynomials
Learning Goal: 1. Write polynomials in factored form
2. Find zeros 3. Write polynomials in standard form given zeros. 4. use multiplicity to describe behavior.
EQ: How can knowing the zeros of a polynomial help to describe the behavior of the polynomial?
Agenda:
Warm up
Notes and examples
Practice together
Practice on your own (finish for HW if necessary.
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree – factors- synthetic division- quadratic formula – zeros – multiplicity-
Binomial Theorem and Pascal’s Triangle (326)

23. Example : you try (𝑎+𝑏 ) 8 you try……. (𝑎+𝑏 ) 8 Common Board Standard:
A- APR.1.1 –understand polynomials are closed under certain operations
F-IF.3.7- describe end behavior of polynomials
Learning Goal: 1. Write polynomials in factored form
2. Find zeros 3. Write polynomials in standard form given zeros. 4. use multiplicity to describe behavior.
EQ: How can knowing the zeros of a polynomial help to describe the behavior of the polynomial?
Agenda:
Warm up
Notes and examples
Practice together
Practice on your own (finish for HW if necessary.
Vocabulary: monomial – degree of monomial – polynomial – degree of polynomial – standard form of polynomial – turning points – end behavior – linear –quadratic – cubic – 4th degree – factors- synthetic division- quadratic formula – zeros – multiplicity-
Example : you try (𝑎+𝑏 ) 8
you try……. (𝑎+𝑏 ) 8

24. Expanding a binomial – remember to use parenthesis
You try (2𝑥−3 ) 4

25. Wednesday Dec 6 Academy DAY 

26. Thursday/Friday December 7 and 8th