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Unit 3 Polynomials

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19. What is a polynomial?

20. Put a polynomial into standard form, identify the degree and leading coefficient

21. Factor polynomial equations completely using one or more of the following methods: factor out a greatest common factor, use the diamond/box method, split the middle, factor the difference of two squares, use substitution to make a complex problem easier.

22. Determine the multiplicity of factors and how it affects the shape of the graph.

23. Understand how the leading coefficient affects end behavior

24. Understand how the degree determines start/end behavior, the number of turns, the number of roots and the number of x-intercepts.

25. Sketch polynomial graphs from factored form without a calculator.

26. Find a polynomial equation in factored form from its graph including the “a”.

quiz

27. Use the quadratic formula to find real and complex roots of polynomials

28. Understand that i =√-1 . Use this to simplify square roots.

29. Use the discriminant to describe the nature of the roots.

30. Use the sum and product of the roots to find a quadratic equation in standard form with integer coefficients

31. Simplify powers of i and perform operations on complex numbers.

32. Solve equations with complex solutions:

28. Use the degree to determine the number of real and complex roots.

Quiz

29. Polynomial division: grid method, synthetic division

30. Using polynomial division to factor.

31. Finding all roots given only an equation and a graph.

32. Factor the sum and difference of two cubes.

33. Synthetic Division (you can use the box method instead)

 

Factoring Higher Power Polynomials
Factoring by Grouping 
Fundamental Theorem of Algebra (and Polynomials)
Polynomial Equations
Polynomial Graphs (zeros, multiplicity, end behavior, graph behavior near roots)

Polynomial Remainder Theorem (and Factor Theorem)

Polynomial Long Division
Synthetic Division

 

Terms and Degree
Finding Zeros on the Calculator
Division of Polynomials
The Remainder and Factor Theorems
Factoring Polynomials Using the Factor Theorem
Methods of Factoring Polynomials
Solving Polynomial Equations
Solving Polynomial Inequalities
Adding Polynomials
Subtracting Polynomials
Multiplying Polynomials
Dividing Polynomials
The Remainder Theorem
Introduction to Polynomial Functions
Characteristics of Polynomial Functions
Graphs of Polynomial Functions in Factored Form
Equations of Polynomial Functions in Factored Form

Factoring Higher Power Polynomials 
Factoring and Perfect Cubes 
Factoring by Grouping 
Polynomial Long Division 
Synthetic Division 
Polynomial Remainder Theorem 
Fundamental Theorem of Algebra 
Polynomial Equations 
Polynomial Identities 
Polynomial Graphs 
(zeros, multiplicity, end behavior, graph 
behavior near roots) 
Practice with Factoring by Grouping 
Practice with Polynomial Division 
Practice with Polynomial Equations 
(multiple choice) 
Practice with More Polynomial Equations 
(solutions shown) 
Practice with Polynomial Identities 
Practice Graphing Polynomial Functions 
Practice Working with Polynomials 
Polynomials (definition, degree, leading term, constant, standard form, closure) 
Polynomials - Add, Subtract, Multiply 
Polynomials - Divide (only monomial or factorable for binomial) 
To refresh basic skills with Factoring 
Polynomials, see Factoring section from 
Algebra 1. 
General Features of Function Graphs 
(intercepts, positive/negative, 
increase/decrease) 
More Features of Function Graphs (continuous, maximum/minimum, symmetry, end behavior) 
Transformations of Functions 
For factoring practice go here
Factoring: 
http://www.phschool.com/webcodes10/index.cfm?wcprefix=aga&wcsuffix=0602&area=view
Complex Numbers: 
http://www.phschool.com/webcodes10/index.cfm?wcprefix=aga&wcsuffix=0506&area=view 
Discriminant: 
http://www.phschool.com/webcodes10/index.cfm?wcprefix=ag 
(Links to an external site.)Links to an external site.a&wcsuffix=0508&area=view (Links to an external site.)Links to an external site. 
Roots: 
http://www.phschool.com/webcodes10/index.cfm?wcprefix=aga&wcsuffix=0605&area=view (Links to an external site.)Links to an external site. 
(SOAP) 
http://www.phschool.com/webcodes10/index.cfm?wcprefix=aga&wcsuffix=0604&area=view (Links to an external site.)Links to an external site. 
(You can use box method here) 
http://www.phschool.com/webcodes10/index.cfm?wcprefix=aga&wcsuffix=0603&area=view (Links to an external site.)Links to an external site. 
Square roots in terms of i 
Powers of i 
Complex conjugate 
Nature of roots of a quadratic 
Sum and product of roots of a quadratic 
Quadratic equation given the sum and product of its roots 
Completing the square 
The quadratic formula 
Factor polynomials completely 
Even and odd functions 

Even and Odd Polynomial Functions
Practice with Factoring by Grouping
Practice with Polynomial Division
Practice with Polynomial Equations (multiple choice)
Practice with More Polynomial Equations (solutions shown)
Practice Graphing Polynomial Functions
Practice Working with Polynomials 
Polynomials (definition, degree, leading term, constant, standard form, closure) 

What is a Polynomial?
 What's the Standard Form of a Polynomial?

 How Do You Find the Degree of a Polynomial?
 What is a Leading Coefficient?

How Do You Determine the Zeros of a Polynomial Function from a Table of Values?

 How Do You Figure Out What Factoring Strategy to Use?
 How Do You Factor a 4-Term Polynomial by Grouping?

 Solving Polynomial Equations

 What is Quadratic Form of a Polynomial Equation?

 How Do You Use a Polynomial Equation to Solve a Word Problem?

 What is the Factor Theorem?

 How Do You Find All the Rational Zeros of a Polynomial Function?

 The Fundamental Theorem of Algebra

 What is the Fundamental Theorem of Algebra?

 What is the Quadratic Formula?
 How Do You Solve a Quadratic Equation With Complex Solutions by Using the Quadratic Formula?

 How was the Quadratic Formula Derived?

How Do You Solve a Word Problem Using the Quadratic Formula?

 How Do You Solve a Quadratic Equation by Using the Quadratic Formula?

 Using the Discriminant

 What is the Discriminant?

 How Do You Find The Discriminant of a Quadratic Equation With 2 Real Solutions?
 How Do You Use The Discriminant to Determine the Number of Real or Complex Solutions to a Quadratic Equation?

 How Do You Find The Discriminant of a Quadratic Equation With 1 Solution?

How Do You Multiply Pure Imaginary Numbers?

 How Do You Simplify the Square Root of a Negative Number?

How Do You Multiply Complex Numbers Using FOIL?

How Do You Divide Complex Numbers Using Conjugates?

How Do You Find Values for x and y to Make Two Complex Numbers Equal?

How Do You Subtract Complex Numbers?

 How can you use trigonometry to represent complex numbers?

How Do You Add Complex Numbers?

 What is the Imaginary Unit i?

 What is an Imaginary Number?

How Do You Find Higher Powers of i?

 Finding all the Zeros of a Polynomial – Example 2

 Finding all the Zeros of a Polynomial – Example 3

 Finding the Formula for a Polynomial Given: Zeros/Roots, Degree, and One Point – Example 1

 Finding the Formula for a Polynomial Given: Zeros/Roots, Degree, and One Point – Example 2

 Finding the Formula for a Polynomial Given: 

Using a polynomial function and its factors solve problems VID

Finding the zeros of a polynomial function

Writing a polynomial from its zeros

Solving polynomial equations by graphing VID

Factoring a sum or difference of cubes

Solving polynomial equations of higher degrees using factoring and the quadratic formula

Solving polynomial equations of higher degrees using factoring

Using the Rational Root Theorem to find roots VID

Solving equations using the Rational Root Theorem

Using the Irrational Root Theorem to find irrational roots

Writing a polynomial from its roots

Using the Fundamental Theorem of Algebra VID

Solving quadratic equations using square roots VID

Solving quadratic equations by factoring VID

Solving quadratic equations using completing the square VID

Solving quadratic equations using completing the square when a ≠ 1

Solving quadratic equations using the quadratic formula VID

Solving real-world problems using the quadratic formula

Choosing the appropriate method to solve quadratic equations 

Using the discriminant to find the number of solutions and solve problems VID

Finding complex solutions VID

Solving quadratic equations using the quadratic formula, complex solution VID

Finding Imaginary Root Theorem VID

 

 

-Polynomial Packet Part I.pdf

-Polynomial Packet Part 2.pdf

-Polynomial Packet Part 3.pdf