Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Factorials

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : Factorials

Simplify the following:

$\frac{(n+2)!}{n!}$

Possible Answers:

(n+2)(n+1)

(n-2)(n-1)

(n+2)(n+1)(n)

Correct answer:

(n+2)(n+1)

Explanation:

To simplify the expression involving factorials, we must remember what a factorial is:

$4! = 4\cdot3\cdot2 \cdot 1 = 24$

For our factorial expression, we can write out some of the terms of the numerator's factorial and we will be able to simplify from there:

$\frac{(n+2)!}{n!}=\frac{(n+2)(n+1)(n)!}{n!}=(n+2)(n+1)$

As you can see, n! remains on top and bottom after writing out the first three terms of the numerator's factorial. There is no need to expand any further once we have the same factorial on top and bottom. They cancel, and we get our final answer.

Report an Error

Example Question #22 : Factorials

Simplify (leave as a product of binomials):

$\frac{(n+2)!}{n!}\cdot \frac{(n+3)!}{(n+1)!}$

Possible Answers:

(n+3)(n+2)^2(n+1)

(n+3)(n+2)(n+1)

(n+2)!(n+1)!(n)!

(n+1)!(n)!

Correct answer:

(n+3)(n+2)^2(n+1)

Explanation:

To simplify the expression, knowing that a factorial is, for example

$n!=(n)\cdot (n-1)\cdot (n-2)\cdot ... \cdot 3\cdot 2\cdot 1$

will make it far easier.

Keeping this in mind, we can rewrite the given expression as

$\frac{(n+2)(n+1)(n!)}{n!}\cdot \frac{(n+3)(n+2)(n+1)!}{(n+1)!}$

which simplifies to

(n+3)(n+2)^2(n+1)

after canceling like terms.

(One does not need to write out all terms of a factorial, rather as many in front that will leave something that cancels with another factorial are the most we usually need!)

Report an Error

Example Question #23 : Factorials

Simplify:

$\frac{(n-3)!}{3!}\cdot \frac{5!}{(n-4)!}$

Possible Answers:

$\frac{n-4}{20}$

20(n-3)

$\frac{20}{n-4}$

$\frac{20(n-3)}{n-4}$

Correct answer:

$\frac{20}{n-4}$

Explanation:

To simplify, remember that a factorial simply means we take the given term and subtract one unit from it successively until we reach 1, and multiply all the terms together:

$n!=n(n-1)(n-2)\cdot...\cdot 3\cdot2\cdot1$

Rewriting our given expression, we get:

$\frac{(n-3)!}{3!} \cdot \frac{5 \cdot4\cdot3!}{(n-4)(n-3)!}$

Notice how we only expanded the factorials as much as we needed to in order to cancel things:

$\frac{5\cdot 4}{n-4}=\frac{20}{n-4}$

Report an Error

Example Question #21 : Factorials

Simplify the expression $\frac{8!}{5!}$

Possible Answers:

336

120

Correct answer:

336

Explanation:

$\frac{8!}{5!}=\frac{8*7*6*5*4*3*2*1}{5*4*3*2*1}$

The 5,4,3,2,1 cancel out leaving 8*7*6 which is 336

Report an Error

Example Question #25 : Factorials

Multiply the factorials: $4!\times 3!$

Possible Answers:

144

$\textup{The answer is not given.}$

169

$4.79\times 10^{8}$

Correct answer:

144

Explanation:

Rewrite the factorials.

$4! = 4\times3\times2\times1 = 24$

$3!=3\times2\times1 = 6$

Multiply these two numbers together.

$24\times 6 = 144$

The answer is: 144

Report an Error

Example Question #22 : Multiplying And Dividing Factorials

Divide the factorials: $\frac{6!}{3!}$

Possible Answers:

720

360

240

120

Correct answer:

120

Explanation:

Expand both factorials in the numerator and denominator.

$\frac{6!}{3!} = \frac{6 \times 5\times4\times3\times2\times1}{3\times2\times1}$

Cancel the common terms on the numerator and denominator.

The numerator becomes:

$6\times 5 \times 4 =120$

The answer is: 120

Report an Error

Example Question #27 : Factorials

Simplify the factorials: $\frac{3!(3!+2!)^2}{5! }$

Possible Answers:

$\frac{32}{5}$

$\frac{16}{5}$

720

$\frac{120}{7}$

Correct answer:

$\frac{16}{5}$

Explanation:

Do not add the factorials!

$3!+2! \neq 5!$

We will need to simplify and rewrite the terms of the factorials.

$\frac{3!(3!+2!)^2}{5!} = \frac{(3\times 2\times 1)[(3\times 2\times 1)+(2\times 1)]^2}{5\times 4\times3\times 2\times 1}$

The common terms in the numerator and denominator can be simplified.

$\frac{[(3\times 2\times 1)+(2\times 1)]^2}{5\times 4}$

Simplify the numerator and denominator.

$\frac{[6+2]^2}{20} = \frac{8^2}{20} = \frac{64}{20} =\frac{4\times 4\times 4}{5\times 4}$

Simplify the fraction by cancelling the common terms.

The answer is: $\frac{16}{5}$

Report an Error

Example Question #28 : Factorials

Solve: $3!(\frac{(4+3)!}{7(5!)})$

Possible Answers:

$\frac{1}{20}$

$\frac{1}{40}$

$\frac{1}{14}$

Correct answer:

Explanation:

Rewrite all the factorial terms in expanded form. To expand a factorial, multiply all the integers in decreasing order until it reaches to one.

$3!(\frac{(4+3)!}{7(5!)}) = (3\times 2\times 1)(\frac{7!}{7(5!)}) = 6(\frac{7!}{7(5!)})$

Do not distribute the integer through the number before the factorial, and do not cancel the sevens in the numerator and denominator.

$7(5!) \neq 35!$

$\frac{7!}{7} \neq 1!$

Rewrite the numerator in terms so that we can simplify the fraction.

$6(\frac{7!}{7(5!)}) = 6(\frac{7\times 6\times5\times4\times3\times2\times1}{7(5\times4\times3\times2\times1)})$

Notice all the constants that we can cancel. This fraction will reduce to"

$6\times 6 = 36$

The answer is:

Report an Error

Example Question #22 : Factorials

Multiply the factorials: $3!\times (2+3)!\times 0!$

Possible Answers:

720

120

1296

Correct answer:

720

Explanation:

Expand the factorials.

$3!\times (2+3)!\times 0! = (3\times 2\times 1)\times 5! \times 0!$

$=(3\times 2\times 1)\times(5\times 4\times 3\times 2\times 1)\times 0!$

Zero factorial is a special case. It is equal to one.

0!=1

The expression becomes:

$=(3\times 2\times 1)\times(5\times 4\times 3\times 2\times 1)$

Multiply all the numbers.

$=6\times 120= 720$

The answer is: 720

Report an Error

Example Question #30 : Factorials

Simplify the factorials: $\frac{2!(3+3)!}{ 3!\times 6}$

Possible Answers:

$\frac{2}{3}$

$\frac{1}{3}$

Correct answer:

Explanation:

Simplify the factorials in the numerator first.

$2!(3+3)! = 2!\cdot 6! =(2\times 1)\cdot (6\times5\times4\times3\times2\times1)$

Simplify the denominator.

$3!\times 6 = (3\times 2\times 1) \times 6$

Eliminate common terms in the numerator and denominator.

The numerator becomes: $2 \times 1\times5\times4 = 40$

The answer is:

Report an Error

View Algebra 2 Tutors

Alejandro
Certified Tutor

Kennesaw State University, Bachelor of Science, Computer Software Engineering.

View Algebra 2 Tutors

Travis
Certified Tutor

Delaware State University, Bachelor of Science, Mathematics.

View Algebra 2 Tutors

Mayowa
Certified Tutor

Logan University, Bachelor of Science, Biology, General.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in Washington DC, MCAT Tutors in Boston, ACT Tutors in Philadelphia, SSAT Tutors in Boston, MCAT Tutors in Philadelphia, ISEE Tutors in San Diego, SAT Tutors in Denver, Math Tutors in Atlanta, SAT Tutors in New York City, LSAT Tutors in Denver

Popular Courses & Classes

Spanish Courses & Classes in Seattle, MCAT Courses & Classes in New York City, SAT Courses & Classes in Miami, MCAT Courses & Classes in Phoenix, GMAT Courses & Classes in Denver, SSAT Courses & Classes in Miami, SSAT Courses & Classes in Los Angeles, GRE Courses & Classes in Denver, GRE Courses & Classes in Los Angeles, GMAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

SAT Test Prep in Denver, GMAT Test Prep in Los Angeles, LSAT Test Prep in Phoenix, SAT Test Prep in Atlanta, MCAT Test Prep in Seattle, MCAT Test Prep in Denver, MCAT Test Prep in San Diego, LSAT Test Prep in Washington DC, ISEE Test Prep in Miami, ACT Test Prep in Dallas Fort Worth

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra II : Factorials

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #21 : Factorials

Example Question #22 : Factorials

Example Question #23 : Factorials

Example Question #21 : Factorials

Example Question #25 : Factorials

Example Question #22 : Multiplying And Dividing Factorials

Example Question #27 : Factorials

Example Question #28 : Factorials

Example Question #22 : Factorials

Example Question #30 : Factorials

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: