|
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?
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?
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
|