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1. Review of Real Numbers(0)

Simplifying Fractions
(0)

Evaluating Exponents
(0)

Evaluating Expressions
(0)

Translating Phrases to Expressions
(0)

Translating Sentences to Equations
(0)

The Distributive Property
(0)

Simplifying Expressions
(0)

2. Linear Equations and Inequalities(0)

The Addition and Subtraction Properties of Equality
(0)

The Multiplication and Division Properties of Equality
(0)

Solving Linear Equations
(0)

Linear Inequalities in One Variable
(0)

3. Solving Word Problems(0)

Introduction to Problem Solving
(0)

Formulas
(0)

Percent Problem Solving
(0)

Mixture Problem Solving
(0)

4. Graphing Linear Equations in Two Variables(0)

The Rectangular Coordinate System
(0)

Graph Linear Equations in Two Variables
(0)

Graph Linear Equations Using Intercepts
(0)

Slope of a Line
(0)

Slope-Intercept Form
(0)

Point Slope Form
(0)

5. Systems of Linear Equations(0)

Solving Systems of Linear Equations by Graphing
(0)

Solving Systems of Linear Equations by Substitution
(0)

Solving Systems of Linear Equations by Elimination
(0)

6. Exponents and Polynomials(0)

The Product Rule
(0)

The Quotient Rule
(0)

Intro to the Power Rules
(0)

The Power of a Quotient Rule
(0)

Negative Exponents
(0)

Simplifying Exponential Expressions Using All Exponent Rules
(0)

Intro to Polynomials
(0)

Adding and Subtracting Polynomials
(0)

Multiplying Polynomials
(0)

Special Products
(0)

7. Factoring(0)

Factoring by Greatest Common Factor & Grouping
(0)

Factoring Trinomials of the Form x² + bx + c
(0)

Factoring Trinomials of the Form ax² + bx + c
(0)

Factoring Special Products
(0)

Quadratic Equations & Applications
(0)

8. Rational Expressions and Equations(0)

Simplifying Rational Expressions
(0)

Multiplying and Dividing Rational Expressions
(0)

Adding and Subtracting Rational Expressions with Common Denominators
(0)

Least Common Denominators
(0)

Adding and Subtracting Rational Expressions with Different Denominators
(0)

Rational Equations
(0)

9. Inequalities and Absolute Value(0)

Set Operations and Compound Inequalities
(0)

Absolute Value Equations
(0)

Absolute Value Inequalities
(0)

Linear Inequalities in Two Variables
(0)

Systems of Linear Inequalities
(0)

10. Relations and Functions(0)

Introduction to Relations and Functions
(0)

Function Notation
(0)

Graphing Common Functions
(0)

Composition of Functions
(0)

Direct & Inverse Variation
(0)

11. Roots, Radicals, and Complex Numbers(0)

Introduction to Radical Expressions
(0)

Simplifying Radical Expressions
(0)

Adding and Subtracting Radicals
(0)

Multiplying, Dividing, and Rationalizing Radicals
(0)

Introduction to Complex Numbers
(0)

Multiplying and Dividing Complex Numbers
(0)

12. Quadratic Equations and Functions(0)

The Square Root Property
(0)

Completing the Square
(0)

The Quadratic Formula
(0)

Graphing Quadratic Equations
(0)

13. Inverse, Exponential, & Logarithmic Functions(0)

Introduction to Inverse Functions
(0)

Exponential Functions
(0)

Introduction to Logarithmic Functions
(0)

Properties of Logarithms
(0)

14. Conic Sections & Systems of Nonlinear Equations(0)

Graphing Circles
(0)

Ellipses
(0)

Parabolas
(0)

Hyperbolas
(0)

15. Sequences, Series, and the Binomial Theorem(0)

Introduction to Sequences
(0)

Arithmetic Sequences
(0)

Geometric Sequences
(0)

Factorials
(0)

15. Sequences, Series, and the Binomial Theorem

Factorials

15. Sequences, Series, and the Binomial Theorem

Factorials: Videos & Practice Problems

Video Lessons Practice Worksheet

28 problems

Problem 1Multiple Choice

Which statement best defines $n!$ ( $n$ factorial)?

Problem 2Multiple Choice

Which explanation correctly justifies why $0 factorial equals 1$ using the recursive identity $n! = n \cdot (n - 1)!$ ?

Problem 3Multiple Choice

Express $7 factorial$ in terms of $5 factorial$ using the recursive identity.

Problem 4Multiple Choice

Simplify $the fraction with numerator 100 factorial and denominator 99 factorial$ .

Problem 5Multiple Choice

Which equality is always true for a positive integer m?

Problem 6Multiple Choice

Compute $the fraction with numerator 12 factorial and denominator 10 factorial$ by choosing the most efficient strategy.

Problem 7Multiple Choice

Which list correctly gives the values of $0 factorial$ , $1 factorial$ , and $2 factorial$ in that order?

Problem 8Multiple Choice

How many distinct linear arrangements (permutations) are there of $6$ distinct books placed on a shelf?

Problem 9Multiple Choice

Which method gives the quickest way to evaluate $the fraction with numerator 15 factorial and denominator 13 factorial$ ?

Problem 10Multiple Choice

Simplify $\frac{(n + 2)!}{n!}$ for a positive integer $n$ . Express your answer in the simplest multiplicative form.

Problem 11Multiple Choice

Evaluate the expression $3! \cdot 2 + 4$ .

Problem 12Multiple Choice

Evaluate $4 times 3 factorial$ .

Problem 13Multiple Choice

Which of the following best describes what $6 factorial$ counts when interpreted as permutations?

Problem 14Multiple Choice

A lottery requires arranging $7$ uniquely numbered balls in an order to win. What is the probability that a single random arrangement matches the winning arrangement?

Problem 15Multiple Choice

Which argument best evaluates the following claim: " $0 factorial$ must be $1$ because assigning any other value would break the identity $n! = n \cdot (n - 1)!$ for $n equals 1$ "?

Problem 16Multiple Choice

Simplify the expression $\frac{(m + 3)!}{m!}$ for integer $m is greater than or equal to 0$ .

Problem 17Multiple Choice

Compute $\frac{10!}{2 \cdot 8!}$ .

Problem 18Multiple Choice

Which of the following gives $2 factorial$ , $3 factorial$ , and $4 factorial$ , respectively?

Problem 19Multiple Choice

Solve for $n$ : $n! = 6 \cdot (n - 1)!$

Problem 20Multiple Choice

For an integer $n is greater than or equal to 3$ , simplify the expression $\frac{n!}{(n - 3)!}$ .

Problem 21Multiple Choice

Simplify $\frac{(n + 4)!}{(n + 1)!}$ , where $n is greater than or equal to 0$ .

Problem 22Multiple Choice

Calculate $\frac{(2 + 3)!}{5}$ .

Problem 23Multiple Choice

How many ordered selections (permutations) are there if $3$ students are chosen and arranged in order from a class of $10$ students? Express using factorial notation and compute the value.

Problem 24Multiple Choice

Given the identity $1! = 1 \cdot 0!$ and the known value $1 factorial equals 1$ , what logical conclusion and justification follows?

Problem 25Multiple Choice

A student calculates $3 factorial positive 4 factorial$ as $open paren 3 plus 4 close paren factorial$ and obtains $5040$ . Identify the error and give the correct value of $3 factorial positive 4 factorial$ .

Problem 26Multiple Choice

Compute $the fraction with numerator 8 factorial and denominator 6 factorial$ .

Problem 27Multiple Choice

A committee of $4$ is to be chosen from $10$ people where order matters for roles (chair, secretary, treasurer, member). Which factorial expression models the number of possible role assignments, and what is the numeric total?

Problem 28Multiple Choice

Which of these is an algebraic simplification of $(n + 2)! - n!$ for integer $n is greater than or equal to 0$ ?