We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Understanding Zeros of a Polynomial

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #13 : Pre Calculus

Factor the polynomial if the expression is equal to zero when $x=-6, -4,\ or\ 2$ .

x^3+8x^2+4x-48

Possible Answers:

(x+4)(x-2)(x-6)

(x-4)(x+2)(x-6)

(x+6)(x+4)(x-2)

(x-4)(x-2)(x+6)

Correct answer:

(x+6)(x+4)(x-2)

Explanation:

Knowing the zeroes makes it relatively easy to factor the polynomial.

The expression (x+6)(x+4)(x-2) fits the description of the zeroes.

Now we need to check the answer.

(x+4)(x-2)=x^2-2x+4x-8=x^2+2x-8

$\small (x^2+2x-8)(x+6)=x^3+6x^2+2x^2+12x-8x-48=x^3+8x^2+4x-48$

We are able to get back to the original expression, meaning that the answer is (x+6)(x+4)(x-2) .

Report an Error

Example Question #14 : Pre Calculus

A polyomial with leading term $x^{3}$ has 6 as a triple root. What is this polynomial?

Possible Answers:

$x ^{3} +216$

$x ^{3} + 18 x^{2}- 108x -216$

$x ^{3} + 18 x^{2}+ 108x +216$

$x ^{3} - 18 x^{2}+ 108x -216$

$x ^{3} -216$

Correct answer:

$x ^{3} - 18 x^{2}+ 108x -216$

Explanation:

Since 6 is a triple root, and the degree of the polynomial is 3, the polynomial is $(x-6)^{3}$ , which we can expland using the cube of a binomial pattern.

$(x-6)^{3} =x ^{3} - 3\cdot x^{2} \cdot 6 + 3\cdot x\cdot 6 ^{2} -6^{3}$

$x ^{3} - 18 x^{2}+ 108x -216$

Report an Error

Example Question #1 : Express A Polynomial As A Product Of Linear Factors

A polyomial with leading term $x^ {3}$ has 5 and 7 as roots; 7 is a double root. What is this polynomial?

Possible Answers:

$x^{3} - 19x^{2} + 119x -245$

$x^{3}+ 17x^{2} +95x +175$

$x^{3}- 17x^{2} +95x -175$

$x^{3} -12x^{2} + 35x$

$x^{3}+ 19x^{2} +119x +245$

Correct answer:

$x^{3} - 19x^{2} + 119x -245$

Explanation:

Since 5 is a single root and 7 is a double root, and the degree of the polynomial is 3, the polynomial is $(x-5)(x-7)^{2}$ . To put this in expanded form:

$(x-7)^{2} = x^{2} - 2 \cdotx\cdot 7 + 7^{2} = x^{2} - 14x + 49$

$(x-5)(x-7)^{2} =(x-5) \left ( x^{2} - 14x + 49 \right )$

$=x \left ( x^{2} - 14x + 49 \right ) -5\left( x^{2} - 14x + 4 9 \right )$

$= x^{3} - 14x^{2} + 49x - \left( 5x^{2} - 70x + 245 \right )$

$= x^{3} - 14x^{2} + 49x - 5x^{2} + 70x -245$

$= x^{3} - 19x^{2} + 119x -245$

Report an Error

Example Question #1 : Understanding Zeros Of A Polynomial

What are the solutions to $y = x^{2} + x -6$ ?

Possible Answers:

x = -6, x = 1

x = 6, x = -1

x = -3, x = 2

x = 3, x = -2

x = 5, x = 1

Correct answer:

x = -3, x = 2

Explanation:

When we are looking for the solutions of a quadratic, or the zeroes, we are looking for the values of such that the output will be zero. Thus, we first factor the equation.

$0 = x^{2} + x - 6 = (x+3)(x-2)$

Then, we are looking for the values where each of these factors are equal to zero.

x + 3 = 0 implies x = -3

and x - 2 = 0 implies x = 2

Thus, these are our solutions.

Report an Error

View Tutors

Wendy
Certified Tutor

Marymount University, Master's/Graduate, Masters of Education.

View Tutors

Priyancka
Certified Tutor

Mithibai College of Arts, Bachelor, Psychology.

View Tutors

Maria Cecilia
Certified Tutor

The University of Texas at El Paso, Bachelor in Arts, Multi-/Interdisciplinary Studies, General. The University of Texas at E...

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Math Tutors in Denver, MCAT Tutors in New York City, ACT Tutors in Chicago, GRE Tutors in Washington DC, Reading Tutors in New York City, Statistics Tutors in Denver, Chemistry Tutors in Los Angeles, Calculus Tutors in Seattle, ACT Tutors in Miami, MCAT Tutors in Boston

Popular Courses & Classes

Spanish Courses & Classes in Miami, GRE Courses & Classes in Seattle, MCAT Courses & Classes in San Diego, GMAT Courses & Classes in Denver, MCAT Courses & Classes in Chicago, ISEE Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Philadelphia, ACT Courses & Classes in Phoenix, LSAT Courses & Classes in Denver, ISEE Courses & Classes in New York City

Popular Test Prep

ACT Test Prep in Phoenix, SSAT Test Prep in New York City, SSAT Test Prep in Washington DC, ISEE Test Prep in Phoenix, SAT Test Prep in Denver, GRE Test Prep in New York City, SSAT Test Prep in Atlanta, SSAT Test Prep in Seattle, ACT Test Prep in Miami, LSAT Test Prep in Philadelphia

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

High School Math : Understanding Zeros of a Polynomial

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #13 : Pre Calculus

Example Question #14 : Pre Calculus

Example Question #1 : Express A Polynomial As A Product Of Linear Factors

Example Question #1 : Understanding Zeros Of A Polynomial

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: