Call Now to Set Up Tutoring:

(888) 888-0446

College Algebra : College Algebra

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 #191 : College Algebra

$\begin{align*}&\text{Simplify the expresssion:}\\&\frac{x^{4}-26x^{3}+151x^{2}+594x-4680}{x^{2}-25x+156}\end{align*}$

Possible Answers:

$x^{2}-9x+27$

$x^{2}-x-30$

$x^{2}+23x+3$

$x^{2}+19x+2$

Correct answer:

$x^{2}-x-30$

Explanation:

$\begin{align*}&\textbf{To perform a polynomial}\\&\textbf{long division, it is often}\\&\textbf{helpful to space terms}\\&\textbf{into columns ordered by power.}\\&\textbf{This includes zero terms.}\\&\textbf{For example: }x^2+0x+5\\&\textbf{When performing each}\\&\textbf{division step, choose a coefficient}\\&\textbf{Which eliminates the highest}\\&\textbf{ordered term each time.}\end{align*}\begin{align*}&&&&&&&&\end{align*}\begin{align*}&&&&&&&&\mathbf{x^{2}}&&\mathbf{-x}&&\mathbf{-30}\\x^{2}&&-25x&&+156|x^{4}&&-26x^{3}&&+151x^{2}&&+594x&&-4680\\&&&&-(x^{4}&&-25x^{3}&&+156x^{2})\\&&&&&&-x^{3}&&-5x^{2}&&+594x\\&&&&&&-(-x^{3}&&25x^{2}&&+-156x)\\&&&&&&&&-30x^{2}&&750x&&+-4680\\&&&&&&&&-(-30x^{2}&&750x&&+-4680)\\\end{align*}$

Report an Error

Example Question #192 : College Algebra

$\begin{align*}&\text{Simplify the expresssion:}\\&\frac{x^{4}+32x^{3}+347x^{2}+1372x+1056}{x^{2}+20x+96}\end{align*}$

Possible Answers:

$x^{2}-17x-20$

$x^{2}+12x+11$

$x^{2}-17x-4$

$x^{2}+21x-19$

Correct answer:

$x^{2}+12x+11$

Explanation:

$\begin{align*}&\textbf{To perform a polynomial}\\&\textbf{long division, it is often}\\&\textbf{helpful to space terms}\\&\textbf{into columns ordered by power.}\\&\textbf{This includes zero terms.}\\&\textbf{For example: }x^2+0x+5\\&\textbf{When performing each}\\&\textbf{division step, choose a coefficient}\\&\textbf{Which eliminates the highest}\\&\textbf{ordered term each time.}\end{align*}\begin{align*}&&&&&&&&\end{align*}\begin{align*}&&&&&&&&\mathbf{x^{2}}&&\mathbf{+12x}&&\mathbf{+11}\\x^{2}&&+20x&&+96|x^{4}&&+32x^{3}&&+347x^{2}&&+1372x&&+1056\\&&&&-(x^{4}&&+20x^{3}&&+96x^{2})\\&&&&&&12x^{3}&&+251x^{2}&&+1372x\\&&&&&&-(12x^{3}&&+240x^{2}&&+1152x)\\&&&&&&&&11x^{2}&&+220x&&+1056\\&&&&&&&&-(11x^{2}&&+220x&&+1056)\\\end{align*}$

Report an Error

Example Question #191 : College Algebra

$\begin{align*}&\text{Simplify the expresssion:}\\&\frac{x^{3}-x^{2}-233x-663}{x^{2}+16x+39}\end{align*}$

Possible Answers:

x-24

x-4

x-17

x+29

Correct answer:

x-17

Explanation:

$\begin{align*}&\textbf{To perform a polynomial}\\&\textbf{long division, it is often}\\&\textbf{helpful to space terms}\\&\textbf{into columns ordered by power.}\\&\textbf{This includes zero terms.}\\&\textbf{For example: }x^2+0x+5\\&\textbf{When performing each}\\&\textbf{division step, choose a coefficient}\\&\textbf{Which eliminates the highest}\\&\textbf{ordered term each time.}\end{align*}\begin{align*}&&&&&&&&\end{align*}\begin{align*}&&&&&&&&\mathbf{x}&&\mathbf{-17}\\x^{2}&&+16x&&+39|x^{3}&&-x^{2}&&-233x&&-663\\&&&&-(x^{3}&&+16x^{2}&&+39x)\\&&&&&&-17x^{2}&&+-272x&&+-663\\&&&&&&-(-17x^{2}&&+-272x&&+-663)\\\end{align*}$

Report an Error

Example Question #192 : College Algebra

$\begin{align*}&\text{Simplify the expresssion:}\\&\frac{x^{3}+2x^{2}-64x+160}{x-4}\end{align*}$

Possible Answers:

$x^{2}-11x-5$

$x^{2}+6x-40$

$x^{2}-23x-12$

$x^{2}+13x-17$

Correct answer:

$x^{2}+6x-40$

Explanation:

$\begin{align*}&\textbf{To perform a polynomial}\\&\textbf{long division, it is often}\\&\textbf{helpful to space terms}\\&\textbf{into columns ordered by power.}\\&\textbf{This includes zero terms.}\\&\textbf{For example: }x^2+0x+5\\&\textbf{When performing each}\\&\textbf{division step, choose a coefficient}\\&\textbf{Which eliminates the highest}\\&\textbf{ordered term each time.}\end{align*}\begin{align*}&&&&&&&&\end{align*}\begin{align*}&&&&\mathbf{x^{2}}&&\mathbf{+6x}&&\mathbf{-40}\\x&&-4|x^{3}&&+2x^{2}&&-64x&&+160\\&&-(x^{3}&&-4x^{2})\\&&&&6x^{2}&&-64x\\&&&&-(6x^{2}&&-24x)\\&&&&&&-40x&&160\\&&&&&&-(-40x&&160)\\\end{align*}$

Report an Error

Example Question #195 : College Algebra

$\begin{align*}&\text{Simplify the expresssion:}\\&\frac{x^{4}-x^{3}-464x^{2}+564x+41040}{x+10}\end{align*}$

Possible Answers:

$x^{3}+14x^{2}-x+5$

$x^{3}-16x^{2}-3x+28$

$x^{3}-11x^{2}-354x+4104$

$x^{3}+3x^{2}+x-16$

Correct answer:

$x^{3}-11x^{2}-354x+4104$

Explanation:

$\begin{align*}&\textbf{To perform a polynomial}\\&\textbf{long division, it is often}\\&\textbf{helpful to space terms}\\&\textbf{into columns ordered by power.}\\&\textbf{This includes zero terms.}\\&\textbf{For example: }x^2+0x+5\\&\textbf{When performing each}\\&\textbf{division step, choose a coefficient}\\&\textbf{Which eliminates the highest}\\&\textbf{ordered term each time.}\end{align*}\begin{align*}&&&&&&&&\end{align*}\begin{align*}&&&&\mathbf{x^{3}}&&\mathbf{-11x^{2}}&&\mathbf{-354x}&&\mathbf{+4104}\\x&&+10|x^{4}&&-x^{3}&&-464x^{2}&&+564x&&+41040\\&&-(x^{4}&&+10x^{3})\\&&&&-11x^{3}&&+-464x^{2}\\&&&&-(-11x^{3}&&+-110x^{2})\\&&&&&&-354x^{2}&&+564x\\&&&&&&-(-354x^{2}&&+-3540x)\\&&&&&&&&4104x&&+41040\\&&&&&&&&-(4104x&&+41040)\\\end{align*}$

Report an Error

Example Question #193 : College Algebra

Perform the following operation: $3x^{2}-2x+1\div x-1$

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

Use synthetic division to for this polynomial

The initial set-up is shown below

$\right 1\rfloor$

First, bring down the leading coefficient:

$\right 1\rfloor$

$\underline{ }$ ______________ ________

Multiply 1, by 3, and then add this to the second column:

$\right 1\rfloor$

$\underline{ }$ ______________ __________

Next, multiply 1, by 1, and add this to the third column:

$\right 1\rfloor$

$\underline{ }$ ______________ __________

Solution: $3x+1+\frac{2}{x-1}$

Report an Error

Example Question #192 : College Algebra

Simplify the following polynomial: $\frac{x^{2}-3x-10}{x+1}$

Possible Answers:

$x-4+\frac{6}{x+1}$

$x-4-\frac{6}{x+1}$

$-x-4-\frac{6}{x+1}$

$x+4-\frac{6}{x+1}$

Correct answer:

$x-4-\frac{6}{x+1}$

Explanation:

$\frac{x^{2}-3x-10}{x+1}$

Determine if there are any common factors between the numerator and the denominator:

$\frac{x^{2}-3x-10}{x+1}=\frac{(x-5)(x+2)}{x+1}$

There are no common factors, so we use synthetic division to simplify the polynomial:

$\right-1 \rfloor$

_________________

Bring down the 1, from the first column:

$\right-1 \rfloor$

_________________

Multiply 1 by -1, and add the product to -3:

$\right-1 \rfloor$

_________________

Multiply -4 by -1, and add the product to -10:

$\right-1 \rfloor$

_________________

Solution:

$\frac{x^{2}-3x-10}{x+1}=$ $x-4-\frac{6}{x+1}$

Report an Error

Example Question #21 : Dividing Polynomials

Divide the polynomial: $\frac{x^2-4x-45}{x^2-12x+27}$

Possible Answers:

$\frac{x-5}{x+3}$

$\frac{x+5}{x-3}$

$\frac{x-9}{x-3}$

$x^2+\frac{1}{3}x -\frac{5}{3}$

$\frac{1}{3}x -\frac{5}{3}$

Correct answer:

$\frac{x+5}{x-3}$

Explanation:

To divide the polynomials, we will first need to factorize the top and bottom.

$\frac{x^2-4x-45}{x^2-12x+27} = \frac{(x-9)(x+5)}{(x-9)(x-3)}$

The answer is: $\frac{x+5}{x-3}$

Report an Error

Example Question #1 : Zeros/Roots Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=- 297x - 270x^{2} - 27\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=1,\frac{1}{10}$

x=-540,-54

$x=-1,-\frac{1}{10}$

x=540,54

Correct answer:

$x=-1,-\frac{1}{10}$

Explanation:

$\begin{align*}&\text{The function }f(x)=- 297x - 270x^{2} - 27\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&-27\cdot (x + 1)\cdot (10x + 1)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-297)\pm\sqrt{(-297)^2-4(-270)(-27)}}{2(-270)}=\frac{297\pm243}{-540}\\&\text{Either way, we find that the function crosses the x-axis at}\ x=-1\text{ and }-\frac{1}{10}.\end{align*}$

Report an Error

Example Question #2 : Zeros/Roots Of A Polynomial

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=- 822x - 288x^{2} - 567\\&\text{has a zero value.}\end{align*}$

Possible Answers:

$x=-\frac{7}{6},-\frac{27}{16}$

x=-972,-672

$x=\frac{7}{6},\frac{27}{16}$

x=972,672

Correct answer:

$x=-\frac{7}{6},-\frac{27}{16}$

Explanation:

$\begin{align*}&\text{Given }f(x)=- 822x - 288x^{2} - 567\text{, to find when it has a value of}\\&\text{zero, we need a method to determine the x values that}\\&\text{make this happen. We can either factor the equation:}\\&-3\cdot (16x + 27)\cdot (6x + 7)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-822)\pm\sqrt{(-822)^2-4(-288)(-567)}}{2(-288)}=\frac{822\pm150}{-576}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=-\frac{7}{6}\text{ and }-\frac{27}{16}.\end{align*}$

Report an Error

View College Algebra Tutors

Daniel
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Psychology.

View College Algebra Tutors

Allyn
Certified Tutor

Indiana Wesleyan University, Master of Science, Business Administration and Management.

View College Algebra Tutors

Brienne
Certified Tutor

Georgia Institute of Technology-Main Campus, Bachelor of Science, Industrial Engineering. Spelman College, Bachelor of Scienc...

All College Algebra Resources

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

Popular Subjects

LSAT Tutors in Washington DC, GRE Tutors in Atlanta, Calculus Tutors in Miami, ISEE Tutors in Chicago, Physics Tutors in Miami, Computer Science Tutors in Boston, Reading Tutors in San Francisco-Bay Area, ACT Tutors in Atlanta, ISEE Tutors in Denver, SSAT Tutors in Atlanta

Popular Courses & Classes

ISEE Courses & Classes in Houston, GRE Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Chicago, GRE Courses & Classes in Philadelphia, ISEE Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Atlanta, ACT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Houston, GMAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

GMAT Test Prep in Los Angeles, GRE Test Prep in Phoenix, ACT Test Prep in Chicago, LSAT Test Prep in Atlanta, LSAT Test Prep in Miami, ACT Test Prep in Houston, ISEE Test Prep in Boston, MCAT Test Prep in Seattle, GRE Test Prep in Denver, GRE Test Prep in Los Angeles

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 : College Algebra

Study concepts, example questions & explanations for College Algebra

All College Algebra Resources

Example Questions

Example Question #191 : College Algebra

Example Question #192 : College Algebra

Example Question #191 : College Algebra

Example Question #192 : College Algebra

Example Question #195 : College Algebra

Example Question #193 : College Algebra

Example Question #192 : College Algebra

Example Question #21 : Dividing Polynomials

Example Question #1 : Zeros/Roots Of A Polynomial

Example Question #2 : Zeros/Roots Of A Polynomial

All College Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: