Polynomial operations
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# Polynomial operations

Learn what you need and when you need it
0.0 (0 ratings)
78 students enrolled
Created by Brian McLogan
Published 12/2012
English
Price: Free
Includes:
• Access on mobile and TV
What Will I Learn?
• Understand How to write and graph a quadratic function
• Understand how to write and graph higher order functions
• Understand how to determine the end behavior of functions
• Understand Complex numbers
• Understand zeros of polynomial functions
• Understand Rational Functions
View Curriculum
Requirements
• An understanding of Algebra
Description

This course is a video lecture course. I will walk through a very common chapter in a pre-calculus course by offering short videos on explanations on how to solve mathematical problems.  Like a standard math class, this course it broken down into sections and types of problems from each section. You should take this course if you need help with Pre-calculus or you need to learn the material and are not currently enrolled in a pre-calculus course

Who is the target audience?
• High School Students
• College Students
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Curriculum For This Course
96 Lectures
00:00
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13 Lectures 00:00
In this video I describe what a quadratic function is and why we give it's name.  There are a few characteristics that define a quadratic function from other functions that we will explore.
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In this video I will explain what the axis of symmetry is and why it is helpful to know when defining and graphing a quadratic.  I will show you the formula for finding the axis of symmetry for any quadratic.
What is an axis of symmetry
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In this video I will show you how to find the vertex of a parabola graphically and alebraically.  The vertex is a very important characteristic of a parabola as it defines the maximum or minimum value of a quadratic function.
What is a vertex
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In this video I will describe the standard form of a quadratic equation.  All quadratics can be written in standard form.  Standard form is helpful for defining the axis of symmetry, vertex and later processes of quadratic functions.
What is Standard form of a quadratic equation
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In this video I will show you how to identify the x-intercepts and vertex of a quadratic function. We will use our knowledge of x-intercepts axis of symmetry and vertex to find these values of our given function.
Identify x-intercepts and vertex of a quadratic ex 1
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In this video I will show you how to identify the x-intercepts and vertex of a quadratic function. We will use our knowledge of x-intercepts axis of symmetry and vertex to find these values of our given function.
Identify x-intercepts and vertex of a quadratic ex 2
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In this video I will show you how to identify the x-intercepts and vertex of a quadratic function. We will use our knowledge of x-intercepts axis of symmetry and vertex to find these values of our given function.
Identify x-intercepts and vertex of a quadratic ex 3
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In this video I will show you how to identify the x-intercepts and vertex of a quadratic function. We will use our knowledge of x-intercepts axis of symmetry and vertex to find these values of our given function.
Identify x-intercepts and vertex of a quadratic ex 4
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In this video I will show you how to identify the x-intercepts and vertex of a quadratic function. We will use our knowledge of x-intercepts axis of symmetry and vertex to find these values of our given function.
Identify x-intercepts and vertex of a quadratic ex 5
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In this video we will look into how to write the equation of a quadratic when given a point and it's vertex.  We will use these values and the vertex form of a parabola to write our equation in standard form.
Writing a quadratic through a point with a given vertex ex 1
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In this video we will look into how to write the equation of a quadratic when given a point and it's vertex.  We will use these values and the vertex form of a parabola to write our equation in standard form.
Writing a quadratic through a point with a given vertex ex 2
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Find the x value of the vertex ex 1
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Find the x value of the vertex ex 2
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Writing, Graphing and polynomial functions
11 Lectures 00:00
In this video we explore what a polynomial function is and what are the characteristics of one. We will use this information for the rest of the course to understand polynomial operations, behavior and graphically qualities
What is a polynomial function?
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I this video we will explore what the zeros of a quadratic function tell us about a polynomial and how we can use them when graphing writing a polynomial.
What do zeros tell us about a polynomial?
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In this video we will explore multiplicity of zeros of a polynomial. Determining multiplicity will help us understand if our zeros will cross or touch at the x-axis. Multiplicity is determined by reviewing the factors of a polynomial.
What does multiplicity of a zero tell us
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In this video we will explore multiplicity of zeros of a polynomial. Determining multiplicity will help us understand if our zeros will cross or touch at the x-axis. Multiplicity is determined by reviewing the factors of a polynomial.
Find the zeros of a polynomial with multiplicity ex 1
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In this video we will explore multiplicity of zeros of a polynomial. Determining multiplicity will help us understand if our zeros will cross or touch at the x-axis. Multiplicity is determined by reviewing the factors of a polynomial.

Find the zeros of a polynomial with multiplicity ex 2
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In this video we will explore multiplicity of zeros of a polynomial. Determining multiplicity will help us understand if our zeros will cross or touch at the x-axis. Multiplicity is determined by reviewing the factors of a polynomial.

Find the zeros of a polynomial with multiplicity ex 3
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In this video we will explore multiplicity of zeros of a polynomial. Determining multiplicity will help us understand if our zeros will cross or touch at the x-axis. Multiplicity is determined by reviewing the factors of a polynomial.

Find the zeros of a polynomial with multiplicity ex 4
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In this video we will explore multiplicity of zeros of a polynomial. Determining multiplicity will help us understand if our zeros will cross or touch at the x-axis. Multiplicity is determined by reviewing the factors of a polynomial.

Find the zeros of a polynomial with multiplicity ex 5
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In this video we will explore how to write a polynomial function when given a set of zeros.  To do this we need to write our zeros as factors and then multiply them to obtain our polynomial.
Find the polynomial function with the given zeros ex 1
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In this video we will explore how to write a polynomial function when given a set of zeros.  To do this we need to write our zeros as factors and then multiply them to obtain our polynomial.
Find the polynomial function with the given zeros ex 2
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In this video we will explore how to write a polynomial function when given a set of zeros.  To do this we need to write our zeros as factors and then multiply them to obtain our polynomial.
Find the polynomial function with the given zeros ex 3
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Determine the left and right hand behavior
5 Lectures 00:00
In this video we will learn how to apply the leading coefficient test to determine the end behavior of polynomials. Understanding the end behavior is very important to identifying and graphing polynomials.
What is the Leading coefficient test?
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In this video we will learn how to apply the leading coefficient test to determine the end behavior of polynomials. Understanding the end behavior is very important to identifying and graphing polynomials.

Determine the left and right hand behavior ex 1
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In this video we will learn how to apply the leading coefficient test to determine the end behavior of polynomials. Understanding the end behavior is very important to identifying and graphing polynomials.

Determine the left and right hand behavior ex 2
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In this video we will learn how to apply the leading coefficient test to determine the end behavior of polynomials. Understanding the end behavior is very important to identifying and graphing polynomials.

Determine the left and right hand behavior ex 3
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In this video we will learn how to apply the leading coefficient test to determine the end behavior of polynomials. Understanding the end behavior is very important to identifying and graphing polynomials.

Determine the left and right hand behavior ex 4
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Complex numbers
22 Lectures 00:00
In this video we will explore what complex numbers are and where they come from.  We will also look at how to apply operations to complex numbers.
What are complex numbers?
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In this video we will explore complex conjugates. Conjugates of binomials are very important because when multiplied together they produce the difference of two squares. When working with complex numbers multiplying by the conjugate allows us to eliminate are imaginary portion of a complex number.
What are complex conjugates?
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In this video we will explore the principal square root of a number. This is where imaginary and complex numbers come from.  This will help in our understanding and reasoning with complex numbers.
What is the principal square root of a number?
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What is the equality of complex numbers?
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Find the real numbers a and b so the equation is true ex 1
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Find the real numbers a and b so the equation is true ex 2
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Write the complex number in standard form ex 1
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Write the complex number in standard form ex 2
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Write the complex number in standard form ex 3
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Addition and subtraction of complex numbers ex 1
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Addition and subtraction of complex numbers ex 2
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Multiplication of complex numbers ex 1
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Multiplication of complex numbers ex 2
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Multiplication of complex numbers ex 3
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Multiplication of complex numbers ex 4
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Multiplication of complex numbers ex 5
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Write the quotient in standard form ex 1
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Write the quotient in standard form ex 2
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Add subtract complex rational numbers ex 1
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Add subtract complex rational numbers ex 2
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Simplify complex numbers ex 1
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Simplify complex numbers ex 2
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Zeros of polynomials
14 Lectures 00:00
What is a zero?

What is the rational zero test?
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What is Descartes rule of signs?
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Find the zeros of a function using the rational zero test ex 1
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Find the zeros of a function using the rational zero test ex 2
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Find the zeros of a function using the rational zero test ex 3
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Find the polynomial function with integer coefficients that has the given zeros ex 1
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Find the polynomial function with integer coefficients that has the given zeros ex 2
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Given a zero find all of the zeros of a function by factoring ex 1
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Given a zero find all of the zeros of a function by factoring ex 2
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Find all of the zeros of the function and write as polynomial factors by factoring ex 1
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Find all of the zeros of the function and write as polynomial factors by factoring ex 2
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Use Descartes Rule of signs to determine the number of positive and negative zeros of a function ex 1
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Use Descartes Rule of signs to determine the number of positive and negative zeros of a function ex 3
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Use Descartes Rule of signs to determine the number of positive and negative zeros of a function ex 3
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Rational functions
11 Lectures 00:00
What is a rational function?
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What is a horizontal asymptote?
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What is the Horizontal asymptote test?
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What is a vertical asymptote?
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What are slant asymptotes?

Identify any horizontal or vertical asymptotes of a rational function ex 1
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Identify any horizontal or vertical asymptotes of a rational function ex 2
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Identify any horizontal or vertical asymptotes of a rational function ex 3
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Identify any horizontal or vertical asymptotes of a rational function ex 4
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Determine the vertical and oblique asymptotes ex 1
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Determine the vertical and oblique asymptotes ex 2
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Determine the vertical and oblique asymptotes ex 3
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Division to find the roots
13 Lectures 00:00
What is the division Algorithm?
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What is long division?
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What is synthetic division?
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What is the remainder theorem?
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What is the factor theorem?
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Use long division to divide ex 1
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Use long division to divide ex 2
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Use long division to divide ex 3
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Using synthetic division to divide ex 1
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Using synthetic division to divide ex 2
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Using synthetic division to divide ex 3
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Given factors complete factorization ex 1
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Given factors complete factorization ex 2
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Given factors complete factorization ex 3

What is Vertex form of a Quadratic Function?

How to complete the square ex 1

How to complete the square ex 2

How to complete the square ex 3