Call Now to Set Up Tutoring:

(888) 888-0446

College Algebra : Polynomial Functions

Study concepts, example questions & explanations for College Algebra

Create An Account

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #7 : Partial Fractions

What is the partial fraction decomposition of the following:

$\frac{1}{x^{2}-3x+2}$

Possible Answers:

$=\frac{1}{x-1}-\frac{2}{x-2}$

$=\frac{1}{x+4}+\frac{2}{x-5}$

$=-\frac{2}{x+3}+\frac{2}{x-10}$

$=\frac{3}{2x-1}+\frac{2}{x+9}$

$=\frac{1}{x-2}-\frac{1}{x-1}$

Correct answer:

$=\frac{1}{x-2}-\frac{1}{x-1}$

Explanation:

Factor the denominator: $x^{2}-3x+2=(x-2)(x-1)$

$\frac{1}{x^{2}-3x+2}=\frac{1}{(x-2)(x-1)}$

$\frac{1}{(x-2)(x-1)}=\frac{A}{x-2}+\frac{B}{x-1}$

Multiply both sides of the equation by (x-2)(x-1)

1=A(x-1)+B(x-2)

Let x=1 :

1=B(1-2)

B=-1

Let x=2 :

1=A(2-1)

A=1

$\frac{1}{(x-2)(x-1)}=\frac{1}{x-2}-\frac{1}{x-1}$

Report an Error

Example Question #101 : Polynomial Functions

Find A and B in the expression

$\frac{x+4}{(x-1)(x+2)} = \frac{A}{x-1}+\frac{B}{x+2}$

Possible Answers:

$A = 5/3 \; ; \; B = -2/3$

$A=4/3 \; ; \; B=2/3$

$A=x \; ; \; B=4$

$A=1 \; ; \; B=4$

Correct answer:

$A = 5/3 \; ; \; B = -2/3$

Explanation:

Take the expression $\frac{x+4}{(x-1)(x+2)} = \frac{A}{x-1}+\frac{B}{x+2}$ and multiply both sides by . This transforms the equation into the following:

x+4=A(x+2)+B(x-1)

To solve for A we want to get rid of the B. So we set x equal to 1:

$1+4 = A(1+3)+B(1-1)\rightarrow 5 = 3A \rightarrow A=5/3$

Similarly, we can get rid of A by setting x equal to -2:

$-2+4=A(-2+2)+B(-2-1)\rightarrow2=-3B\rightarrow B=-2/3$

Report an Error

View College Algebra Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

View College Algebra Tutors

Charles
Certified Tutor

Pacific Intercontinental College, Master's/Graduate, Mathematics.

View College Algebra Tutors

Jeremy
Certified Tutor

The University of Alabama, Bachelor in Arts, Religious Studies. University of West Alabama, Master of Arts, Social Sciences.

All College Algebra Resources

5 Diagnostic Tests 84 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

French Tutors in Los Angeles, Chemistry Tutors in San Diego, SSAT Tutors in San Diego, MCAT Tutors in Washington DC, Biology Tutors in Miami, Chemistry Tutors in Miami, ISEE Tutors in Philadelphia, MCAT Tutors in Dallas Fort Worth, Reading Tutors in San Diego, Spanish Tutors in Miami

Popular Courses & Classes

MCAT Courses & Classes in Chicago, ACT Courses & Classes in Seattle, Spanish Courses & Classes in Houston, LSAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Washington DC, SAT Courses & Classes in Boston, MCAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Denver, GRE Courses & Classes in Boston, SSAT Courses & Classes in Seattle

Popular Test Prep

SSAT Test Prep in New York City, LSAT Test Prep in Houston, GRE Test Prep in Atlanta, SSAT Test Prep in San Diego, SAT Test Prep in Houston, ACT Test Prep in Seattle, GRE Test Prep in San Francisco-Bay Area, GRE Test Prep in Denver, SAT Test Prep in Los Angeles, MCAT Test Prep in Chicago

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

College Algebra : Polynomial Functions

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #7 : Partial Fractions

Example Question #101 : Polynomial Functions

All College Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: