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 #82 : Polynomial Functions

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=15 - 76x^{2} - 281x\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=\frac{1}{19},-\frac{15}{4}$

$x=\frac{4}{19},-15$

$x=-\frac{1}{19},\frac{15}{4}$

$x=\frac{42423}{152},\frac{43001}{152}$

Correct answer:

$x=\frac{1}{19},-\frac{15}{4}$

Explanation:

$\begin{align*}&\text{The function }f(x)=15 - 76x^{2} - 281x\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&-(4x + 15)\cdot (19x - 1)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-281)\pm\sqrt{(-281)^2-4(-76)(15)}}{2(-76)}=\frac{281\pm289}{-152}\\&\text{Either way, we find thatthe function crosses the x-axis at} \ x=\frac{1}{19}\text{ and }-\frac{15}{4}.\end{align*}$

Report an Error

Example Question #85 : Polynomial Functions

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=- 435x - 84x^{2} - 450\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=-15,-\frac{40}{7}$

$x=-\frac{15}{4},-\frac{10}{7}$

$x=\frac{15}{4},\frac{10}{7}$

$x=\frac{24295}{56},\frac{24425}{56}$

Correct answer:

$x=-\frac{15}{4},-\frac{10}{7}$

Explanation:

$\begin{align*}&\text{The function }f(x)=- 435x - 84x^{2} - 450\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&-3\cdot (4x + 15)\cdot (7x + 10)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(-435)\pm\sqrt{(-435)^2-4(-84)(-450)}}{2(-84)}=\frac{435\pm195}{-168}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=-\frac{15}{4}\text{ and }-\frac{10}{7}.\end{align*}$

Report an Error

Example Question #86 : Polynomial Functions

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=199x + 200x^{2} - 28\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=-\frac{1}{8},\frac{28}{25}$

$x=\frac{1}{2},-\frac{112}{25}$

$x=\frac{1}{8},-\frac{28}{25}$

$x=-\frac{79351}{400},-\frac{79849}{400}$

Correct answer:

$x=\frac{1}{8},-\frac{28}{25}$

Explanation:

$\begin{align*}&\text{The function }f(x)=199x + 200x^{2} - 28\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&(25x + 28)\cdot (8x - 1)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(199)\pm\sqrt{(199)^2-4(200)(-28)}}{2(200)}=\frac{-199\pm249}{400}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=\frac{1}{8}\text{ and }-\frac{28}{25}.\end{align*}$

Report an Error

Example Question #87 : Polynomial Functions

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=348x + 96x^{2} + 270\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=-10,-\frac{9}{2}$

$x=\frac{5}{2},\frac{9}{8}$

$x=-\frac{5}{2},-\frac{9}{8}$

$x=-\frac{5557}{16},-\frac{5579}{16}$

Correct answer:

$x=-\frac{5}{2},-\frac{9}{8}$

Explanation:

$\begin{align*}&\text{The function }f(x)=348x + 96x^{2} + 270\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&6\cdot (2x + 5)\cdot (8x + 9)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(348)\pm\sqrt{(348)^2-4(96)(270)}}{2(96)}=\frac{-348\pm132}{192}\\&\text{Either way, we find thatthe function crosses the x-axis at} \ x=-\frac{5}{2}\text{ and }-\frac{9}{8}.\end{align*}$

Report an Error

Example Question #88 : Polynomial Functions

$\begin{align*}&\text{Find the value(s) of x where the function: }f(x)=251x - 33x^{2} - 400\\&\text{crosses the x-axis.}\end{align*}$

Possible Answers:

$x=\frac{64}{3},\frac{100}{11}$

$x=-\frac{16667}{66},-\frac{16465}{66}$

$x=\frac{16}{3},\frac{25}{11}$

$x=-\frac{16}{3},-\frac{25}{11}$

Correct answer:

$x=\frac{16}{3},\frac{25}{11}$

Explanation:

$\begin{align*}&\text{The function }f(x)=251x - 33x^{2} - 400\text{ crosses the x-axis}\\&\text{when it has a value of zero. To find the x values that}\\&\text{satisfy this, we can either factor the equation:}\\&-(11x - 25)\cdot (3x - 16)\\&\text{or, if this is not intuitive, use the quadratic formula:}\\&\frac{-b\pm\sqrt{b^2-4ac}}{2a}(\text{for equations of the form: }a^2x+bx+c)\\&\frac{-(251)\pm\sqrt{(251)^2-4(-33)(-400)}}{2(-33)}=\frac{-251\pm101}{-66}\\&\text{Either way, we find thatthe function crosses the x-axis at}\ x=\frac{16}{3}\text{ and }\frac{25}{11}.\end{align*}$

Report an Error

Example Question #83 : Polynomial Functions

Find the zeros of the given polynomial:

2x^2-2x-15=0

Possible Answers:

$x=\frac{-5}{2},\frac{3}{2}$

x=-3,-5

x=-5,3

$x=\frac{1\pm \sqrt{31}}{2}$

x=3,-5

Correct answer:

$x=\frac{1\pm \sqrt{31}}{2}$

Explanation:

To find the values for in which the polynomial equals , we first want to factor the equation:

2x^2-2x-15=0

$x=\frac{-(-2)\pm \sqrt{(-2)^2-4(2)(-15)}}{2(2)}$

$\\x=\frac{2\pm \sqrt{4+120}}{4}$

$x=\frac{2\pm \sqrt{124}}{4}$

$x=\frac{2\pm 2\sqrt{31}}{4}$

$x=\frac{1\pm \sqrt{31}}{2}$

Report an Error

Example Question #11 : Finding Zeros Of A Polynomial

Consider the polynomial

$P(x) = 3x^{5}+ 6x^{3} + 17x^{2} + 7x + 10$

By Descartes' Rule of Signs alone, how many positive real zeroes does P(x) have?

(Note: you are not being asked for the actual number of positive real zeroes.)

Possible Answers:

Two or Zero

Zero

One or three

Five

One

Correct answer:

Zero

Explanation:

By Descartes' Rule of Signs, the number of sign changes - changes from positive to negative coefficient signs - in P(x) gives the maximum number of positive real zeroes; the actual number of positive real zeroes must be that many or differ by an even number.

If the polynomial

$P(x) = 3x^{5}+ 6x^{3} + 17x^{2} + 7x + 10$

is examined, it can be seen that there are no changes in sign from term to term; all coefficients are positive. Therefore, there can be no positive real zeroes.

Report an Error

Example Question #91 : Polynomial Functions

Consider the polynomial

$p(x) = x^{6}+ 6x^{4} -8x^{2}+ 1$

Which of the following is true of the rational zeroes of ?

Hint: Think "Rational Zeroes Theorem".

Possible Answers:

The only rational zeroes of are and 1.

has at least one rational zero, but neither nor 1 is a zero.

has no rational zeroes.

The only rational zero of is 1.

The only rational zero of is .

Correct answer:

The only rational zeroes of are and 1.

Explanation:

By the Rational Zeroes Theorem, any rational zeroes of a polynomial must be obtainable by dividing a factor of the constant coefficient by a factor of the leading coefficient. Since both values are equal to 1, and 1 has only 1 as a factor, this restricts the set of possible rational zeroes to the set $\left \{ -1, 1\right \}$ .

Both values can be tested as follows:

1 is a zero of if and only if p(1) =0 . An easy test for this is to add the coefficients and determine whether their sum, which is p(1) , is 0:

$p(x) = x^{6}+ 6x^{4} -8x^{2}+ 1$

p(1)= 1+6-8+1 = 0

1 is indeed a zero.

is a zero of if and only if p(-1) =0 . An easy test for this is to add the coefficients after changing the sign of the odd-degree coefficients, and determine whether their sum, which is p(-1) , is 0. However, as their are no odd-degree coefficients, the sum is the same:

$p(x) = x^{6}+ 6x^{4} -8x^{2}+ 1$

p(-1)= 1+6-8+1 = 0

is also a zero.

Report an Error

Example Question #92 : Polynomial Functions

Determine the zeros of the following equation: y= x^2-5x-14

Possible Answers:

-2,7

14,5

-2,-7

-7,2

2,7

Correct answer:

-2,7

Explanation:

To determine the zeros of this equation, we will need to factorize the polynomial.

The only common factors of that will give us a middle term of negative by addition or subtraction is:

y= x^2-5x-14 = (x+2)(x-7)

Set each binomial equal to zero and solve.

x+2 = 0; x= -2

x-7=0; x=7

The zeros are: -2,7

Report an Error

Example Question #261 : College Algebra

Determine the partial fraction decomposition of

$\frac{x+4}{x^2-1}$

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

First we need to factor the denominator.

$\frac{x+4}{(x-1)(x+1)}$

Now we can rewrite it as such

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

Now we need to get a common denominator.

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

Now we set up an equation to figure out and .

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

To solve for , we are going to set x=1 .

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

$5=2A\rightarrow A=\frac{5}{2}$

To find , we need to set x=-1

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

$3=-2B\rightarrow B=-\frac{3}{2}$

Thus the answer is:

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

Report an Error

View College Algebra Tutors

Alejandro
Certified Tutor

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

View College Algebra Tutors

Tracy
Certified Tutor

Clarion University of Pennsylvania, Bachelor of Science, Physics.

View College Algebra Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

All College Algebra Resources

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

Popular Subjects

MCAT Tutors in Denver, GMAT Tutors in Philadelphia, Math Tutors in New York City, GRE Tutors in Boston, English Tutors in Boston, ACT Tutors in Atlanta, English Tutors in Philadelphia, SAT Tutors in Chicago, Physics Tutors in Seattle, Spanish Tutors in Denver

Popular Courses & Classes

ISEE Courses & Classes in Los Angeles, GRE Courses & Classes in New York City, GRE Courses & Classes in Houston, MCAT Courses & Classes in San Diego, MCAT Courses & Classes in Phoenix, ACT Courses & Classes in Chicago, SSAT Courses & Classes in New York City, LSAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Denver, LSAT Courses & Classes in Chicago

Popular Test Prep

LSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Seattle, LSAT Test Prep in Phoenix, SAT Test Prep in Phoenix, MCAT Test Prep in Chicago, MCAT Test Prep in Atlanta, SAT Test Prep in Dallas Fort Worth, ISEE Test Prep in New York City, ISEE Test Prep in Denver, SSAT Test Prep in San Diego

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 #82 : Polynomial Functions

Example Question #85 : Polynomial Functions

Example Question #86 : Polynomial Functions

Example Question #87 : Polynomial Functions

Example Question #88 : Polynomial Functions

Example Question #83 : Polynomial Functions

Example Question #11 : Finding Zeros Of A Polynomial

Example Question #91 : Polynomial Functions

Example Question #92 : Polynomial Functions

Example Question #261 : College Algebra

All College Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: