College Algebra Explained

In this lesson, we review the product and power rules for exponents.

Practice test for the product and power rules for exponents.

This quiz will test your ability to work with the product and power rules for exponents.

In this lesson, we will review the basic definition of a polynomial. We will learn how to identify a monomial, binomial, and trinomial. We will also learn how to find the degree of a term and the degree of a polynomial.

Practice test for what is a polynomial.

This quiz will test your understanding of the definition of a polynomial.

In this lesson, we will learn how to add and subtract polynomials.

Practice test for adding and subtracting polynomials.

This quiz will test your ability to add and subtract polynomials.

In this lesson, we will learn how to multiply polynomials. We will cover how to multiply a monomial by a polynomial. We will also learn how to find the product of two binomials using FOIL. Lastly, we will learn how to multiply more complex polynomials together.

Practice test for multiplying polynomials.

This quiz will test your ability to multiply polynomials.

In this lesson, we will learn how to find frequently occurring polynomial products using special products formulas.

Practice test for special polynomial products.

This quiz will test your ability to find commonly occuring binomial products, more often called "special products".

In this lesson, we will learn how to divide polynomials.

Practice test for dividing polynomials.

This quiz will test your ability to divide polynomials using long division.

In this lesson, we learn how to divide polynomials using synthetic division.

Practice test for synthetic division

This quiz will test your ability to divide polynomials using synthetic division.

This quiz will test your knowledge of how to perform operations with polynomials.

In this lesson, we will learn how to identify the GCF or greatest common factor for a group of monomial terms. We will then learn how to factor out the GCF from a polynomial.

Practice test for factoring out the greatest common factor.

This quiz will test your ability to find and factor out the GCF (Greatest Common Factor) from a polynomial.

In this lesson, we will learn how to factor a four-term polynomial using the grouping method.

Practice test for factoring by grouping.

This quiz will test your ability to factor a four-term polynomial using grouping.

In this lesson, we will learn how to factor trinomials with a leading coefficient of 1 into the product of two binomials.

Practice test for factoring trinomials when the leading coefficient is 1.

This quiz will test your ability to factor a trinomial when the leading coefficient is 1.

In this lesson, we will learn how to factor trinomials when the leading coefficient is not 1, using the AC Method (factoring by grouping).

Practice test for factoring trinomials using the ac method.

This quiz will test your ability to factor trinomials using the AC Method.

In this lesson, we will learn how to factor trinomials when the leading coefficient is not 1, using the reverse FOIL method.

Practice test for factoring trinomials using reverse foil (trial and error).

This quiz will test your ability to factor trinomials using reverse FOIL.

In this lesson, we will learn how to factor commonly occuring polynomials using special factoring formulas.

Practice test for special factoring.

This quiz will test your ability to factor commonly occuring polynomials using special factoring formulas.

In this lesson, we will learn how to factor polynomials using substitution.

Practice test for factoring by substitution.

This quiz will test your ability to factor polynomials that are quadratic in form, using substitution.

This quiz will test your knowledge of how to factor a polynomial.

In this lesson, we will review how to find the restricted values for a rational expression.

Practice test for finding the restricted value for a rational expression.

This quiz will test your ability to find the restricted values for a rational expression.

In this lesson, we will review how to simplify a rational expression.

Practice test for simplifying rational expressions.

This quiz will test your ability to simplify rational expressions.

In this lesson, we will review how to multiply and divide rational expressions.

Practice test for multiplying and dividing rational expressions.

This quiz will test your ability to multiply and divide rational expressions.

In this lesson, we will review how to find the LCD for a group of rational expressions

Practice Test for finding the lcd for rational expressions.

This quiz will test your ability to find the LCD for rational expressions.

In this lesson, we will review how to find the LCD for a group of rational expressions, along with how to add and subtract rational expressions.

Practice test for adding and subtracting rational expressions.

This quiz will test your ability to add and subtract rational expressions.

In this lesson, we will review how to simplify complex rational expressions.

Practice test for complex rational expressions.

This quiz will test your ability to simplify complex rational expressions.

This quiz will test your knowledge of rational expressions.

In this lesson, we will review how to simplify negative exponents. We will also review how to use the quotient rule for exponents.

Practice test for negative exponents and the quotient rule.

This quiz will test your ability to simplify expressions using negative exponents and the quotient rule for exponents.

In this lesson, we will review how to simplify expressions with rational exponents.

Practice test for rational exponents (fractional exponents).

This quiz will test your ability to write radical expressions in exponential form, using radical exponents.

In this lesson, we will review how to evaluate radical expressions. We will also look at how to deal with radicals that involve variables in the radicand.

Practice test for radical expressions.

This quiz will test your ability to evaluate a radical expression.

In this lesson, we will review how to simplify radical expressions.

Practice test for simplifying radical expressions.

This quiz will test your ability to simplify radical expressions.

In this lesson, we will review how to add and subtract radical expressions.

Practice test for operations with radical expressions.

This quiz will test your ability to perform operations with radical expressions.

In this lesson, we will review how to rational the denominator.

Practice test for rationalizing denominators.

This quiz will test your ability to rationalize a denominator.

This quiz will test your knowledge of radical expressions, simplifying negative exponents, and using rational exponents.

In this lesson, we will review the addition property of equality. This property will allow us to add or subtract the same number to or from both sides of an equation.

Practice test for the addition property of equality.

This quiz will test your knowledge of how to solve one-step equations using addition and subtraction.

In this lesson, we will review the multiplication property of equality. This property will allow us to multiply or divide both sides of an equation by the same non-zero number.

Practice test for the multiplication property of equality.

This quiz will test your knowledge of how to solve equations using the multiplication property of equality.

In this lesson, we will review the four-step process used to solve any linear equation in one variable.

Practice test for solving linear equations in one variable.

This quiz will test your knowledge of how to solve a linear equation in one variable. 

Practice test for solving linear equations with fractions or decimals practice test

This quiz will test your knowledge of how to solve equations with Fractions or Decimals.

In this lesson, we will review how to determine if an equation is conditional, a contradiction (no solution), or an identity (can be solved with any real number).

Practice test for identifying types of equations.

This quiz will test your ability to determine if an equation is conditional, a contradiction, or an identity.

In this lesson, we review how to solve proportion equations and proportion word problems.

Practice test for solving proportion equations.

This quiz will test your ability to solve proportion equations.

In this lesson, we review how to solve literal equations. A literal equation is one that contains more than one unique variable. When we solve a literal equation, we are solving for a specific variable. Another way to think of this is we are putting our equation in terms of one of the variables.

Practice test for solving literal equations.

This quiz will test your knowledge of how to solve an equation for a specified variable (solving literal equations).

In this lesson, we will review how to solve a linear inequality in one variable.

Practice test for solving linear inequalities in one variable.

This quiz will test your knowledge of how to solve a linear inequality in one variable.

In this lesson, we will review how to solve a three-part inequality.

Practice test for solving a three-part inequality in one variable.

This quiz will test your knowledge of how to solve a three-part inequality in one variable.

In this lesson, we will learn how to solve compound inequalities with the connective words "and" or "or".

Practice test for solving compound inequalities with "and" or "or".

This quiz will test your knowledge of how to solve a compound inequality with "and" or "or".

In this lesson, we learn how to solve absolute value equations.

Practice test for solving absolute value equations.

This quiz will test your knowledge of how to solve an absolute value equation.

In this lesson, we will review how to solve absolute value inequalities.

Practice test for solving absolute value inequalities.

This quiz will test your knowledge of how to solve absolute value inequalities.

In this quiz, we will test our knowledge of how to solve linear equations and inequalities in one variable.

In this lesson, we review how to translate phrases into algebraic expressions and equations.

Practice test for translating phrases into algebraic expressions.

In this lesson, we will review how to solve word problems with consecutive integers.

Practice test for consecutive integer word problems.

In this quiz, we will test your knowledge of how to solve consecutive integer problems.

In this lesson, we review how to solve age word problems.

Practice test for age word problems.

In this quiz, we will test your knowledge of how to solve age word problems.

In this lesson, we review how to solve motion word problems.

Practice test for motion word problems.

In this quiz, we will test your knowledge of how to solve motion word problems.

In this lesson, we will review how to solve mixture word problems.

Practice test for mixture word problems.

In this quiz, we will test your knowledge of how to solve mixture word problems.

In this lesson, we review how to solve bill and coin word problems, which are also referred to as money word problems.

Practice test for money word problems.

In this quiz, we will test our knowledge of how to solve word problems that involve money, such as bills or coins.

In this lesson, we review the process used to solve a word problem with the simple interest formula: I = prt.

Practice test for simple interest word problems.

In this quiz, we test your knowledge of how to solve simple interest word problems.

In this lesson, we review how to solve word problems that involve percentages.

Practice test for percent word problems.

This quiz will test your knowledge of how to solve percent word problems.

Practice test for the imaginary unit i.

This quiz will test your knowledge of how to find the square root of a negative number using the imaginary unit i. We will also test your knowledge of how to simplify powers of i.

This lesson will review how to perform operations with complex numbers.

Practice test for operations with complex numbers.

This quiz will test your knowledge of how to perform operations with complex numbers.

In this lesson, we review how to simplify with powers of i.

Practice test for simplifying powers of i.

This quiz will test your knowledge of how to simplify powers of i.

In this lesson, we review how to solve quadratic equations by factoring.

Practice test for solving quadratic equations by factoring.

In this lesson, we learn how to solve a quadratic equation of the form: x^2 = k or (ax + b)^2 = k. This property will be the foundation for our next lesson on completing the square.

Practice test for the square root property.

In this lesson, we will review how to solve a quadratic equation by completing the square.

Practice test for completing the square.

In this lesson, we will review how to solve quadratic equations using the quadratic formula.

Practice test for the quadratic formula.

In this lesson, we review how to solve equations that are quadratic in form. This means we can use substitution to write the equation as a quadratic equation. We can then solve the equation and substitute again to find our answer.

Practice test for quadratic in form.

In this lesson, we learn how to set up and solve common application problems that involve quadratic equations.

Practice test for applications of quadratic equations.

In this lesson, we review how to solve quadratic inequalities.

Practice test for solving quadratic inequalities.

This quiz will test your understanding of how to solve quadratic equations and inequalities.

In this lesson, we review how to solve radical equations. Here will will focus on how to solve equations with square roots. We will look at equations with higher level roots in part II.

Practice test for solving radical equations I.

This quiz will test your knowledge of how to solve radical equations.

In this lesson, we will continue to review the process used for solving radical equations. We will look at examples with cube roots, fourth roots, and mixed roots.

Practice test for solving radical equations II.

This quiz will test your knowledge of how to solve radical equations.

In this lesson, we review the process of solving a radical inequality.

Practice test for solving radical inequalities I.

This quiz will test your knowledge of how to solve radical inequalities.

In this lesson, we continue to review solving radical inequalities.

Practice test for solving radical inequalities II.

This quiz will test your knowledge of how to solve a radical inequality.

In this lesson, we review how to solve rational equations.

Practice test for solving rational equations.

This quiz will test your knowledge of how to solve rational equations.

In this lesson, we review how to solve a radical inequality.

Practice test for solving rational inequalities.

This quiz will test your knowledge of how to solve rational inequalities.

In this lesson, we review word problems that involve rational equations. The problem types we will cover are known as work rate problems and motion word problems.

Practice test for applications of rational equations.

This quiz will test your knowledge of how to solve word problems that involve solving rational equations.

This quiz will test your knowledge of how to solve radical equations, rational equations and inequalities.

In this lesson, we learn how to solve absolute value equations with quadratic and rational expressions involved.

Practice test for absolute value equations II.

This quiz will test your knowledge of how to solve more advanced absolute value equations.

In this lesson, we learn how to solve more advanced absolute value equations. We will look at nested absolute value equations, equations with double absolute value operations and a lose number, and a more advanced quadratic equation with absolute value involved.

Practice test for absolute value equations III.

This quiz will test your knowledge of more challenging absolute value equations.

In this lesson, we learn how to solve more advanced absolute value inequalities.

Practice test for absolute value inequalities II.

This quiz will test your knowledge of more advance absolute value inequalities.

This quiz will test your knowledge of how to solve more advanced absolute value equations/inequalities.

In this lesson, we review the coordinate plane and how to plot ordered pairs.

Practice test for the rectangular coordinate system.

This quiz will test your knowledge of the rectangular coordinate plane and how to plot ordered pairs.

In this lesson, we learn how to find the distance between two points using the distance formula. The distance formula is a direct application of the pythagorean formula, which relates the sides of a right triangle. a^2 + b^2 = c^2

Practice test for finding the distance between two points.

This quiz will test your knowledge of how to find the distance between two points on the coordinate plane.

In this lesson, we learn how to determine if three points are the vertices of a right triangle.

Practice test for determining whether three points are the vertices of a right triangle.

This quiz will test your knowledge of how to determine if three points are the vertices of a right triangle.

In this lesson, we learn how to determine if three points are collinear, using the distance formula.

Practice test for determining whether three points are collinear.

This quiz will test your knowledge of how to determine if three points are collinear.

In this lesson, we learn how to find the midpoint of a line segment.

Practice test for the midpoint formula.

This quiz will test your knowledge of the midpoint formula.

Practice test for plotting complex numbers.

This quiz will test your knowledge of how to plot complex numbers on the complex plane.

Practice test for finding the absolute value of a complex number.

In this lesson, we learn how to find the absolute value of a complex number.

In this lesson, we learn how to find the distance between two complex numbers on the complex plane. Additionally, we will learn how to find the midpoint of a line segment that has two complex numbers as endpoints.

Practice test for distance and midpoint formulas in the complex plane.

This quiz will test your knowledge of how to work with the distance and midpoint formulas in the complex plane.

In this lesson, we will learn how to write the equation of a circle in center-radius form, and graph a circle on the coordinate plane.

Practice test for graphing circles.

This quiz will test your knowledge of how to graph circles.

This quiz will test your knowledge of the coordinate plane, the distance formula,  working with complex numbers on the complex plane and circles.

In this lesson, we learn about relations and functions. We will also introduce the concept of domain and range.

Practice test for relations and functions.

This quiz will test your knowledge of how to determine if a relation is a function.

In this lesson, we will review how to find the domain and range of a relation.

Practice test for domain and range.

This quiz will test your knowledge of how to find the domain and range of a relation or function.

In this lesson, we learn how to graphically determine if a relation is a function using the vertical line test.

Practice test for the vertical line test.

This quiz will test your knowledge of how to use the vertical line test to determine if we have a function.

In this lesson, we learn how to write a function using function notation. Additionally, we will understand how to use function notation to evaluate a function for a given value of the independent variable.

Practice test for Function Notation.

This quiz will test your knowledge of function notation.

In this lesson, we learn how to graph a linear function using the traditional method of creating a table of values. We then move on and show a faster method that involves graphing the line from slope-intercept form.

Practice test for graphing linear functions.

This quiz will test your knowledge of how to graph linear functions.

In this lesson, we learn how to find the slope of a line using the slope formula. Additionally, we will learn how to place a line in slope-intercept form and determine the slope of a line from its equation.

Practice test for finding the slope of a line.

This quiz will test your knowledge of how to find the slope of a line.

In this lesson, we learn how to write the equation of a line in slope intercept form, point-slope form, and standard form.

Practice test for equations of lines.

This quiz will test your knowledge of how to manipulate the equation of a line into its different forms: slope-intercept form, point-slope form, and standard form.

In this lesson, we learn how to determine if two lines are parallel, perpendicular, or neither.

Practice test for parallel and perpendicular lines.

This quiz will test your knowledge of how to determine if two lines are parallel, perpendicular, or neither.

This quiz will test your knowledge of the basics of functions, along with topics of linear functions.

In this lesson, we learn about the graphs of six basic functions, along with their domain and range.

Practice test for graphs of basic functions.

This quiz will test your knowledge of how to graph basic functions.

In this lesson, we learn about the absolute value function, the greatest integer function and piecewise-defined functions.

Practice test for piecewise functions.

This quiz will test your knowledge of piecewise functions.

In this lesson, we will learn how to find the intervals where a function is increasing, decreasing, or constant from its graph.

Practice test for increasing, decreasing, and constant functions.

This quiz will test your knowledge of increasing, decreasing, and constant functions.

In this lesson, we will learn about stretching or shrinking a graph.

Practice test for graphing techniques: shrinking and stretching.

This quiz will test your knowledge of stretching or shrinking a graph.

In this lesson, we will learn how to reflect a graph across an axis.

Practice test for graphing techniques: reflecting.

This quiz will test your knowledge of graphing using reflecting.

In this lesson, we will learn how to determine if a function is even, odd, or neither.

Practice test for even and odd functions.

This quiz will test your knowledge of how to determine if a function is even or odd.

In this lesson, we learn about horizontal and vertical shifts, which are also known as translations.

Practice test for graphing techniques: translations (horizontal and vertical shifts).

This quiz will test your knowledge of translations, otherwise known as horizontal and vertical shifts.

In this lesson, we learn how to perform operations (addition, subtraction, multiplication, and division) with functions.

Practice test for operations on functions.

This quiz will test your knowledge of how to perform operations with functions.

In this lesson, we learn how to find the difference quotient.

Practice test for the difference quotient.

This quiz will test your knowledge of how to find the difference quotient.

In this lesson, we learn how to compose functions, decompose functions, and find the domain of a composite function.

Practice test for composition of functions.

This quiz will test your knowledge of function composition.