Intermediate Algebra
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Factoring
Factoring out the greatest common factor (GCF) of an expression
Factoring an expression using the "grouping" method
Factoring trinomials with leading coefficients of 1
Illustration of the ac-method of factoring
Factoring a perfect-square trinomial
Factoring a difference of squares
Factoring a difference of cubes
Factoring an expression involving multiple factoring techniques
Rational expressions and equations
Evaluating a rational expression
Simplifying a rational expression
Finding the domain of a rational expression
Issues encountered with cancelling common factors
Multiplying rational expressions
Expressing numerical fractions in terms of their least common denominator
Expressing rational expressions in terms of their LCD
Adding and subtracting rational expressions
Simplifying a complex rational expression (method 1)
Simplifying a complex rational expression (method 2)
Discussing differences between rational expressions versus rational equations
Fundamentals of functions
Determining the domain and range of a relation
Determine the domain and range of a relation from its graph
Understanding the concept of a function and how to evaluate a function
Evaluating a function for specified domain values
Understanding how to determine the domain of a function
Understanding how to determine the domain of a function (example 2)
Understanding how to determine the domain of a function (example 3)
Finding the domain of a function algebraically
Discussing the vertical line test
Applying the vertical line test to a graph
Determining the domain and range of a function given its graph
Determining intercepts of the graphs of functions
Determining intercepts of the graphs of functions (example 2)
Discussing when an equation represents a function
Variation
Discussing the concept of direct variation
Discussing the concept of inverse variation
Discussing the concept of joint variation
Illustrating the use of merging multiple variation models into one scenario
Compound linear inequalities
Discussing the concepts of intersection and union (of sets)
Discussing a compound linear inequality involving the word "and"
Discussing a compound linear inequality involving the word "or"
Discussing patterns when determining solution sets for compound linear inequalities
Linear equations and inequalities involving absolute value
Discussing the concept of linear equations involving absolute value (part 1)
Discussing the concept of linear equations involving absolute value (part 2)
Solving a linear equation with two terms involving absolute value
Discussing linear inequalities involving absolute value (part 1)
Discussing linear inequalities involving absolute value (part 2)
Solving linear inequalities involving absolute value
Graphing linear inequalities in two variables
Graphing a linear inequality (method #1)
Graphing a linear inequality (method #2)
Fundamentals of radicals
Discussing nth roots of real numbers (part 1)
Discussing nth roots of real numbers (part 2)
Discussing nth roots of real numbers (part 3)
Simplifying basic radical expressions
Discussing functions with radicals (part 1)
Graphing a function containing a radical
Expressing radicals using exponent notation (part 1)
Expressing radicals using exponent notation (part 2)
Converting between radical notation and exponent notation
Simplifying an expression involving rules for working with exponents
Adding and/or subtracting radical expressions
Adding and subtracting radical expressions requiring the simplification of the radicals
Multiplying radicals involving the same index (assume all variables represent nonnegative quantities!!)
Multiplying radical expressions involving different indices (assume all variables represent nonnegative quantities!!)
Multiplying radical expressions involving previously learned "patterns"
Rationalizing denominators with one term (part 1)
Rationalizing denominators with one term (part 2)
Rationalizing denominators with two terms (part 1)
Rationalizing denominators with two terms (part 2)
Solving radical equations involving one radical expression
Solving radical equations involving two radical expressions
Fundamentals of complex numbers
Discussing the structure of the complex number system
Discussing the pattern with the powers of i
Simplifying square roots involving negative radicands
Adding and subtracting complex numbers
Solving quadratic equations
Solving a quadratic equation by factoring
Discussing the square root property
Discussing perfect square trinomials
Discussing the concept of completing the square (part 1)
Discussing the concept of completing the square (part 2)
Applying the procedure of completing the square to solving quadratic equations
Solving a quadratic equation by completing the square
Solving a quadratic equation by completing the square (example 2)
Solving a quadratic equation by completing the square (example 3)
Solving a quadratic equation by completing the square (example 4)
Deriving the quadratic formula
Solving a quadratic equation using the quadratic formula
Solving a quadratic equation in nonstandard form using the quadratic formula
Solving a quadratic equation via the quadratic formula
Knowing when common factors can be cancelled
Solving an equation having quadratic form (part 1)
Solving an equation having quadratic form (part 2)
Circles
Calculating the distance between two points
Deriving the standard form of a circle
Sketching graphs of circles in standard form
Writing the equation of a circle (given in expanded form) in standard form
Determining the equation of a circle in standard form
Graphing quadratic functions
Discussing the vertex form of a quadratic function
Graphing quadratic functions in vertex form
Converting a quadratic function from standard form to vertex form
Deriving the vertex formula (part 1)
Deriving the vertex formula (part 2)
Using the vertex formula to convert a quadratic function (written in standard form) to vertex form