# College Algebra Explained

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## What you'll learn

- Review of Basic Concepts: Real Numbers, Order of Operations, Number Line, Absolute Value
- Review of Polynomials: Adding, Subtracting, Multiplying, Dividing, Synthetic Division, Factoring
- Review of Rational Expressions: Lowest Terms, Undefined, Addition, Subtraction, Multiplication, Division, Complex Fractions
- Review of Radical Expressions: Radical Notation, Simplifying a Radical, Operations with Radicals, Rationalizing Denominators
- Solving Linear Equations and Inequalities
- Solving Application of Linear Equations Problems (Word Problems)
- Solving Absolute Value Equations and Inequalities
- Working with Complex Numbers
- Solving Quadratic Equations and Inequalities
- Solving Applications of Quadratic Equations (Word Problems)
- Solving Rational Equations and Inequalities
- Solving Radical Equations and Inequalities
- The Rectangular Coordinate Plane
- The Complex Coordinate Plane
- Distance and Midpoint Formulas
- Relations and Functions
- Domain and Range
- Function Notation, Function Composition, Operations on Functions
- Graphing Linear Equations
- Linear Equations, Finding the Slope of a Line and Equations of Lines
- Graphing Circles
- Graphing Elementary Functions
- Graphing Transformations
- Solving Systems of Linear Equations in Two Variables
- Solving Systems of Linear Equations in Three Variables
- Solving Word Problems with Linear Systems
- Using Curve Fitting to Find an Equation Through Three Points
- Partial Fraction Decomposition
- Solving Linear Systems using Gaussian Elimination and Gauss-Jordan Elimination
- Matrix Algebra
- Adding and Subtracting Matrices
- Solving Matrix Equations
- Multiplying a Matrix by a Scalar
- Multiplying Matrices
- Finding the Inverse of a Matrix
- Solving Linear Systems using Matrix Inverses
- Determine if functions are one-to-one using the horizontal line test
- Determine if functions are one-to-one algebraically
- Find the Inverse of a One-to-One Function
- Find the Inverse of a Domain Restricted One-to-One Function
- Graphing the Inverse of a Function
- Graphing an Exponential Function
- Solving Exponential Equations with Like Bases
- Solving Compound Interest Word Problems
- Graphing Logarithmic Functions
- Properties of Logarithms | Condensing Logarithms | Expanding Logarithms
- Change of Base Rule for Logarithms
- Solving Exponential and Logarthimic Equations
- Finding the Vertex Form of a Parabola
- How to Graph a Parabola
- Remainder Theorem
- Using the Remainder Theorem to Test Zeros for a Polynomial Function
- The Factor Theorem
- Using the Factor Theorem to Factor a Polynomial Function Given One Zero
- The Rational Zeros Theorem
- The Fundamental Theorem of Algebra
- The Number of Zeros Theorem
- Writing Polynomial Equations Given Zeros and a Point
- Conjugate Zeros Theorem
- Descartes' Rule of Signs
- Intermediate Value Theorem
- Boundedness Theorem
- Finding the upper and lower bounds for the real zeros of a polynomial function
- Solving NonLinear Systems of Equations
- Conic Sections: Parabolas - Focus and Directrix
- Conic Sections: Ellipses - Finding the Foci and Graphing
- Sequences
- Arithmetic Sequences
- Geometric Sequences
- Arithmetic Series
- Geometric Series
- Finding the Common Difference in an Arithmetic Sequence
- Evaluating an Arithmetic Series
- The Binomial Theorem
- Combinations
- Permutations
- Counting Theory
- Probability
- Angles in Trigonometry
- Complementary Angles
- Supplementary Angles
- Determine if two angles are coterminal angles
- Finding Angle measures for similar triangles
- Finding side lengths for similar triangles
- Finding the Trigonometric Function Values of an Angle
- Finding Trigonometric Function Values Given One Value and the Quadrant
- Finding Trigonometric Function Values Based on Reciprocal Identities
- Finding Trigonometric Function Values Based on Pythagorean Identities
- Finding Trigonometric Function Values Based on Quotient Identities
- Finding Trigonometric Function Values of Acute Angles
- Writing a Trigonometric Function in terms of its Cofunction
- Solving Trigonometric Equations Using Cofunction Identities

## Requirements

- Basic Arithmetic (Addition, Subtraction, Multiplication, Division)
- Pre-Algebra (Must Have)
- Basic Algebra (Algebra 1) (Must Have)
- Intermediate Algebra (Algebra 2) (Highly Suggested)

## Description

Become a Master of **College Algebra** & **Trigonometry **and** Ace** your next Algebra **Exam**! In this course, you will master all concepts of** Algebra **and **Trigonometry**,** **from** beginner **to** advanced,** with our **step-by-step** video tutorials and** test **your knowledge with over **2500 Practice Test Questions**. The concepts you will learn are fundamental to success in higher math classes such as Calculus and Linear Algebra. The topics of the course include:

Review of Real Numbers

Operations with Polynomials

Factoring Polynomials

Rational Expressions

Rational Exponents

Radical Expressions

Solving Linear Equations/Inequalities

Solving Word Problems with Linear Equations

Complex Numbers

Solving Quadratic Equations (Factoring, Completing the Square, Quadratic Formula)

Solving Word Problems with Quadratic Equations

Solving Quadratic/Rational Inequalities

Solving Radical Equations/Inequalities

Solving Advanced Absolute Value Equations/Inequalities

The Coordinate Plane

Graphing Circles

Distance and Midpoint Formulas

Relations and Functions

Domain and Range

Vertical Line Test

Increasing, Decreasing, Constant Intervals

Graphing Linear Functions

Slope

Forms of a Line

Graphs of Basic Equations (Parent Functions)

Graphing Transformations

Function Operations

The Difference Quotient

Composition of Functions

Solving Linear Systems in Two/Three Variables

Solving Systems of Linear Inequalities in Two Variables

Solving Word Problems with Linear Systems

Curve Fitting, Finding the Equation of a Parabola Given Three Points

Partial Fraction Decomposition

Solving Linear Systems using Gaussian Elimination and Gauss-Jordan Elimination

Matrix Algebra (Adding Matrices, Multiplying Matrices, Solving Matrix Equations)

Finding the Inverse of a Matrix

Solving Linear Systems using the Inverse of a Matrix

Finding the Determinant of a Matrix

Finding the Inverse of a Matrix Using Cofactors

Solving Linear Systems using Cramer's Rule

Applications of determinants: Area of a Triangle, test for collinearity, equation of a line

Determine if functions are one-to-one using the Horizontal line test/algebraic methods

Finding the Inverse of a One-to-One Function

Finding the Inverse of a Domain Restricted Function

Graphing the Inverse of a Function

Graphing Exponential Functions

Solving Exponential Equations with Like Bases

Solving Compound Interest Word Problems

Solving Continuous Compound Interest Word Problems

Graphing Logarithmic Functions

Properties of Logarithms

Expanding Logarithms

Condensing Logarithms

Change of Base Rule for Logarithms

Solving Exponential and Logarithmic Equations

Finding the Vertex Form of a Parabola

How to Graph a Parabola

The Remainder Theorem

Using the Remainder Theorem to test for Zeros of a Polynomial Function

The Factor Theorem

Using the Factor Theorem to factor a polynomial function given one zero

Using the Rational Zeros Theorem to find all possible rational zeros

The Fundamental Theorem of Algebra and the Number of Zeros Theorem

Writing Polynomial Functions Given Zeros and a Point

Conjugate Zeros Theorem

Descartes' Rule of Signs

Intermediate Value Theorem

Boundedness Theorem

Find the upper and lower bounds for zeros of a polynomial function

Solving nonlinear systems of equations

Conic Sections: Parabolas - Focus and Directrix

Conic Sections: Ellipses - Finding the Foci and Graphing

Arithmetic Sequences

Arithmetic Series

Geometric Sequences

Geometric Series

The Binomial Theorem

Counting Theory

Combinations

Permutations

Probability

Angles in Trigonometry

Complementary and Supplementary Angles

Working with Degrees, Minutes, and Seconds

Converting between Decimal Degrees and Degrees, Minutes, and Seconds

Determine if two angles are coterminal angles

Finding angle measures for similar triangles

Finding side lengths for similar triangles

Finding the Trigonometric Function Values of an Angle

Finding the Trigonometric function Values of an Angle Given a Point on the Terminal Side

Finding Trigonometric Function Values Given One Value and the Quadrant

Finding Trigonometric Function Values Based on Pythagorean Identities

Finding Trigonometric Function Values Based on Quotient Identities

Finding Trigonometric Function Values of Acute Angles

Writing Trigonometric Functions in Terms of its Cofunction

Solving Trigonometric Equations Using Cofunction Identities

## Who this course is for:

- Students who need a complete understanding of Advanced Algebra
- Students currently enrolled in a College Level Algebra Course
- Students currently enrolled in a Pre-Calculus Course
- Students who need to master Algebra in order to fully prepare for Calculus

## Course content

- Preview18:56
- 00:06Classifying Real Numbers Practice Test
- 5 questionsClassifying Real Numbers
- 18:26Exponents and the Order of Operations (PEMDAS)
- 00:07Exponents and the Order of Operations Practice Test
- 5 questionsExponents and the Order of Operations (PEMDAS)
- 15:14Ratios, Rates, and Proportions
- 00:06Ratios, Rates, and Proportions Practice Test
- 5 questionsRatios, Rates, and Proportions
- 23:59Properties of Real Numbers
- 00:06Properties of Real Numbers Practice Test
- 5 questionsProperties of Real Numbers
- 14 questionsClassifying Real Numbers, Exponents / PEMDAS, Ratios, Properties of Real Numbers
- 22:39Inequalities, the Number Line, and Interval Notation
- 00:07Inequalities, the Number Line, and Interval Notation Practice Test
- 5 questionsInequalities, the Number Line, and Interval Notation
- 16:41Absolute Value and the Distance Between Two Points on a Number Line
- 00:07Absolute Value and the Distance Between Two Points Practice Test
- 5 questionsAbsolute Value and the Distance Between Two Points on a Number Line
- 12 questionsOrder and Absolute Value