We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Algebra II

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 #42 : Intermediate Single Variable Algebra

Find the zeros.

f(x)=2x^5-8x^3+8x

Possible Answers:

$x=0, \sqrt{2}, -\sqrt{2 }$

x=2,0

$x=\sqrt{2}$

x=0

$x= \sqrt{-2}}$

Correct answer:

$x=0, \sqrt{2}, -\sqrt{2 }$

Explanation:

Factor the equation to 2x(x^4-4x^2+4) . Set 2x=0 and get one of your 's to be . Then factor the second expression to (x^2-2) (x^2-2) . Set them equal to zero and you get $\pm \sqrt{2}$ .

Report an Error

Example Question #4 : Factoring Polynomials

Factor the following polynomial:

54a^3b-2b^4

Possible Answers:

2b(3a-b)(9a^2+2ab+b^2)

3b(3a-b)(9a^2+3ab+b^2)

2b(3a-b)(9a^2+3ab+b^2)

2b(2a-b)(9a^2+3ab+b^2)

3b(2a-b)(9a^2+3ab+b^2)

Correct answer:

2b(3a-b)(9a^2+3ab+b^2)

Explanation:

Begin by extracting from the polynomial:

54a^3b-2b^4

=2b(27a^3-b^3)

Now, factor the remainder of the polynomial as a difference of cubes:

=2b(3a-b)(9a^2+3ab+b^2)

Report an Error

Example Question #2 : Factoring Polynomials

Factor the following polynomial:

5ab+b^2+5ac-c^2

Possible Answers:

(b+c)(5a+b+c)

(b-c)(5a+b-c)

(b-c)(5a-b+c)

(b+c)(5a-b-c)

(b+c)(5a+b-c)

Correct answer:

(b+c)(5a+b-c)

Explanation:

Begin by rearranging like terms:

5ab+b^2+5ac-c^2

=5ab+5ac+b^2-c^2

Now, factor out like terms:

=5a(b+c)+(b+c)(b-c)

Rearrange the polynomial:

=(b+c)(5a+b-c)

Report an Error

Example Question #3 : Factoring Polynomials

Factor the following polynomial:

m^3-3m^2a+3ma^2-a^3

Possible Answers:

m-a

(m-a)^3

(m-a)^4

(m-a)^2

Correct answer:

(m-a)^3

Explanation:

Begin by rearranging like terms:

m^3-3m^2a+3ma^2-a^3

=m^3-a^3-3m^2a+3ma^2

Now, factor out like terms:

=(m-a)(m^2+ma+a^2)-3ma(m-a)

Rearrange the polynomial:

=(m-a)(m^2-2ma+a^2)

Factor:

=(m-a)(m-a)^2

=(m-a)^3

Report an Error

Example Question #2 : Factoring Polynomials

Factor the following polynomial:

12n^2-7n-10

Possible Answers:

(3n-5)(3n+3)

(4n-5)(3n+2)

(4n+5)(3n-2)

(4n-5)(4n+2)

(3n-5)(3n+2)

Correct answer:

(4n-5)(3n+2)

Explanation:

Begin by separating -7n into like terms. You do this by multiplying and , then finding factors which sum to

12n^2-7n-10

12n^2-15n+8n-10

Now, extract like terms:

3n(4n-5)+2(4n-5)

Simplify:

(4n-5)(3n+2)

Report an Error

Example Question #11 : Factoring Polynomials

Factor the following polynomial:

(3a-4b)^2-(a+3b)^2

Possible Answers:

(4a-b)(2a+7b)

(4a+b)(2a-7b)

(4a-2b)(2a-7b)

(4a-b)(2a-7b)

(4a+b)(2a+7b)

Correct answer:

(4a-b)(2a-7b)

Explanation:

To begin, distribute the squares:

(3a-4b)^2-(a+3b)^2

[(3a-4b)+(a+3b)][(3a-4b)-(a+3b)]

Now, combine like terms:

(4a-b)(2a-7b)

Report an Error

Example Question #11 : Factoring Polynomials

Factor the following polynomial:

5x^3y+40y^4

Possible Answers:

y(x+2y)(x^2-2xy+4y^2)

3y(x+2y)(x^2-2xy+4y^2)

4y(x+2y)(x^2-2xy+4y^2)

5y(x+2y)(x^2-2xy+4y^2)

2y(x+2y)(x^2-2xy+4y^2)

Correct answer:

5y(x+2y)(x^2-2xy+4y^2)

Explanation:

Begin by extracting from the polynomial:

5x^3y+40y^4

5y(x^3+8y^3)

Now, distribute the cubic polynomial:

5y(x+2y)(x^2-2xy+4y^2)

Report an Error

Example Question #12 : Factoring Polynomials

Factor the following polynomial:

x^5-x^3y^2+27y^5-27x^2y^3

Possible Answers:

(x+y)(x-y)(x-3y)(x^2-3xy+9y^2)

(x+y)(x+y)(x-3y)(x^2+3xy+9y^2)

(x+y)(x-y)(x+3y)(x^2+3xy+9y^2)

(x-y)(x-y)(x-3y)(x^2+3xy+9y^2)

(x+y)(x-y)(x-3y)(x^2+3xy+9y^2)

Correct answer:

(x+y)(x-y)(x-3y)(x^2+3xy+9y^2)

Explanation:

Begin by extracting like terms:

x^5-x^3y^2+27y^5-27x^2y^3

x^3(x^2-y^2)+27y^3(y^2-x^2)

Now, rearrange the right side of the polynomial by reversing the signs:

x^3(x^2-y^2)-27y^3(x^2-y^2)

Combine like terms:

(x^2-y^2)(x^3-27y^3)

Factor the square and cubic polynomial:

(x+y)(x-y)(x-3y)(x^2+3xy+9y^2)

Report an Error

Example Question #31 : Intermediate Single Variable Algebra

Factor the following polynomial:

x^2-9-6xy+9y^2

Possible Answers:

(x-3y-3)(x-3y-3)

(x-3y+3)(x-3y-3)

(x-3y+3)(x+3y-3)

(x+3y+3)(x-3y-3)

(x+3y+3)(x+3y+3)

Correct answer:

(x-3y+3)(x-3y-3)

Explanation:

Begin by rearranging the terms to group together the quadratic:

x^2-9-6xy+9y^2

(x^2-6xy+9y^2)-9

Now, convert the quadratic into a square:

(x-3y)^2-9

Finally, distribute the :

(x-3y+3)(x-3y-3)

Report an Error

Example Question #11 : Factoring Polynomials

Factor the following polynomial:

m^4n+m^2n-mn^4-mn^2

Possible Answers:

mn(m-n)(m^2+mn+n^2+1)

mn(m-n)(m^2-mn+n^2+1)

mn(m-n)(m^2+mn+n^2-1)

mn(m+n)(m^2+mn+n^2+1)

mn(m-n)(m^2+mn-n^2+1)

Correct answer:

mn(m-n)(m^2+mn+n^2+1)

Explanation:

Begin by extracting from the polynomial:

m^4n+m^2n-mn^4-mn^2

mn(m^3+m-n^3-n)

Now, rearrange to combine like terms:

mn(m^3-n^3+m-n)

Extract the like terms and factor the cubic:

mn[(m-n)(m^2+mn+n^2)+1(m-n)]

Simplify by combining like terms:

mn(m-n)(m^2+mn+n^2+1)

Report an Error

View Tutors

Jennifer
Certified Tutor

Texas Woman's University, Bachelor of Education, Education. Houston Baptist University, Master of Arts, Psychology.

View Tutors

Franco
Certified Tutor

University of Western Ontario, Bachelor in Arts, English. Brock University, Masters in Education, Education.

View Tutors

Brandie
Certified Tutor

Full Sail University, Bachelor of Fine Arts, Creative Writing. Full Sail University, Master of Fine Arts, Creative Writing.

All High School Math Resources

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

Popular Subjects

GMAT Tutors in Washington DC, LSAT Tutors in Los Angeles, Algebra Tutors in Los Angeles, Spanish Tutors in Houston, Algebra Tutors in Phoenix, Reading Tutors in Seattle, GMAT Tutors in Phoenix, Statistics Tutors in Philadelphia, Computer Science Tutors in San Francisco-Bay Area, SSAT Tutors in Atlanta

Popular Courses & Classes

GMAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Boston, MCAT Courses & Classes in Washington DC, GMAT Courses & Classes in Philadelphia, ACT Courses & Classes in Philadelphia, ISEE Courses & Classes in Denver, ACT Courses & Classes in Miami, MCAT Courses & Classes in Atlanta, Spanish Courses & Classes in San Diego, LSAT Courses & Classes in Washington DC

Popular Test Prep

ACT Test Prep in Philadelphia, GMAT Test Prep in Phoenix, GRE Test Prep in Denver, GRE Test Prep in Houston, LSAT Test Prep in Chicago, SAT Test Prep in Dallas Fort Worth, ACT Test Prep in Boston, SAT Test Prep in Washington DC, ACT Test Prep in Denver, LSAT Test Prep in Boston

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 : Algebra II

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #42 : Intermediate Single Variable Algebra

Example Question #4 : Factoring Polynomials

Example Question #2 : Factoring Polynomials

Example Question #3 : Factoring Polynomials

Example Question #2 : Factoring Polynomials

Example Question #11 : Factoring Polynomials

Example Question #11 : Factoring Polynomials

Example Question #12 : Factoring Polynomials

Example Question #31 : Intermediate Single Variable Algebra

Example Question #11 : Factoring Polynomials

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: