Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #12 : Factoring Polynomials

Factor the following expression:

x^2 - 11x + 10

Possible Answers:

(x-5)(x+2)

(x-10)(x-1)

(x-2)(x-5)

(x-10)(x+1)

(x-5)(x-5)

Correct answer:

(x-10)(x-1)

Explanation:

x^2 - 11x + 10

To factor, we are looking for two terms that multiply to give and add together to get .

Possible factors of :

$(1,10),\ (-1,-10),\ (2,5),\ (-2,-5)$

Based on these options, it is clear our factors are and .

$(-1)(-10)=10\ \text{and}\ (-1)+(-10)=-11$

Our final answer will be:

(x-10)(x-1)

Report an Error

Example Question #3 : Factoring Polynomials

Factor the following expression:

x^2 + 20x + 96

Possible Answers:

(x - 12)(x-8)

(x+24)(x+4)

(x + 2)(x-48)

(x + 6)(x+16)

(x + 12)(x+8)

Correct answer:

(x + 12)(x+8)

Explanation:

x^2 + 20x + 96

To factor, we are looking for two terms that multiply to give and add together to get . There are numerous factors of , so we will only list a few.

Possible factors of :

$(3,32),\ (-3,-32),\ (4,24),\ (-4,-24),\ (6,16),\ (8,12)$

Based on these options, it is clear our factors are and .

$(8)(12)=96\ \text{and}\ 8+12=20$

Our final answer will be:

(x + 12)(x+8)

Report an Error

Example Question #13 : Factoring Polynomials

Factor the following expression:

x^2 -38x -600

Possible Answers:

(x-60)(x+10)

(x-50)(x+12)

(x-300)(x+2)

(x-50)(x-12)

(x-100)(x+6)

Correct answer:

(x-50)(x+12)

Explanation:

x^2 -38x -600

To factor, we are looking for two terms that multiply to give and add together to get . There are numerous factors of , so we will only list a few.

Possible factors of :

$(2,-300),\ (3,-200),\ (5,-120),\ (6,-100),\ (10,-60),\ (12,-50),\ (15,-40)$

Based on these options, it is clear our factors are and .

$(12)(-50)=-600\ \text{and}\ 12+(-50)=-38$

Our final answer will be:

(x-50)(x+12)

Report an Error

Example Question #14 : Factoring Polynomials

Factor the following expression:

x^2 - 26x + 105

Possible Answers:

(x - 5)(x-21)

(x + 7)(x-15)

(x - 5)(x+21)

(x - 7)(x-15)

(x + 7)(x-21)

Correct answer:

(x - 5)(x-21)

Explanation:

x^2 - 26x + 105

To factor, we are looking for two terms that multiply to give 105 and add together to get .

Possible factors of 105 :

$(3,35),\ (-3,-35),\ (5,21),\ (-5,-21),\ (7,15),\ (-7,-15)$

Based on these options, it is clear our factors are and .

$(-5)(-21)=105\ \text{and}\ (-5)+(-21)=-26$

Our final answer will be:

(x - 5)(x-21)

Report an Error

Example Question #15 : Factoring Polynomials

Simplify:

$\frac{x^2+6x+9}{x+3}$

Possible Answers:

$\frac{(x+3)}{(x-3)}$

x+6x+3

x+15

x+3

Correct answer:

x+3

Explanation:

Factor the numerator:

$x^2+6x+9\rightarrow (x+3)(x+3)$

Simplify the fraction:

$\frac{(x+3)(x+3)}{(x+3)}\rightarrow (x+3)$

Report an Error

Example Question #21 : Factoring Polynomials

Factor:

x^3-6x^2+9x

Possible Answers:

x(x^2-6x+9)

x(x+3)(x-3)

x^2(x-3)

x(x-3)(x-3)

(x-9)(x+1)

Correct answer:

x(x-3)(x-3)

Explanation:

Factor:

x^3-6x^2+9x

Step 1: Factor out

x(x^2-6x+9)

Step 2: Factor the polynomial

x(x-3)(x-3)

Report an Error

Example Question #22 : Factoring Polynomials

Factor:

x^2+5x-14

Possible Answers:

(x-2)(x+7)

(x+7)(x-7)

(x+5)(x+2)

(x+14)(x-1)

(x-8)(x+8)

Correct answer:

(x-2)(x+7)

Explanation:

Factor:

x^2+5x-14

When factoring a polynomial ax^2+bx+c , the product of the coefficients must be , the sum of the factors must be , and the product of the factors must be .

For the above equation, a=1 , b=5 , and c=-14 .

Set up the factor equation:

$(x+{\color{Red} ?})(x+{\color{Red} ?})$

Becauase is negative, one of the factors must be negative as well. Because is positive, this means the larger factor is positive as well.

Two numbers that meet these requirements are and . Their product is , and their sum is .

(x-2)(x+7)

Report an Error

Example Question #23 : Factoring Polynomials

Expand:

(x+3)(x-9)

Possible Answers:

x^2+6x-3

x^2-6x-27

x^2-12x-27

x^2+6x-9

x^2+3x+9

Correct answer:

x^2-6x-27

Explanation:

Follow the FOIL rule when multiplying - first, outside, inside, last.

First: $x\cdot x=x^2$

Oustide: $x\cdot -9=-9x$

Inside: $3\cdot x=3x$

Last: $3\cdot -9=-27$

Add all of these together:

x^2-9x+3x-27

Combine like terms:

${\color{Red} x^2-6x-27}$

Report an Error

Example Question #24 : Factoring Polynomials

Solve x^2 +x=12 algebraically.

Possible Answers:

x=-3 or x=4

x=-3

x=-4

x=4 or x=6

x=2 or x=-6

Correct answer:

x=-3 or x=4

Explanation:

Subtract 12 from both sides:

x^2+x-12=0

Factor:

(x+3)(x-4)=0

Then, by the zero-product property,

x+3=0 or x-4=0 .

Solve:

x=-3 or x=4

Report an Error

Example Question #25 : Factoring Polynomials

Factor the following equation:

x^2+7x+12=0

Possible Answers:

(x+3)(x+4)

(x-6)(x+2)

(x+3)(x+3)

(x-4)(x-3)

(x+12)(x+1)

Correct answer:

(x+3)(x+4)

Explanation:

Factor: x^2+7x+12

The last term is positive, which indicates that both factors should be positive:

$(x{\color{Red} +}?)(x{\color{Red} +}?)$

The sum of the factors must be , and their product must be .

This means the factors are and

Therefore:

${\color{Red} (x+3)(x+4)}$

Report an Error

View Algebra 2 Tutors

Mariam
Certified Tutor

Yarmouk University, Bachelor of Science, Mathematics. Touro College, Master of Science, Teacher Education, Multiple Levels.

View Algebra 2 Tutors

Brian
Certified Tutor

Cornell University, Bachelor of Science, Biology, General. Rutgers University-New Brunswick, Doctor of Medicine, Molecular Me...

View Algebra 2 Tutors

Abe
Certified Tutor

CUNY Brooklyn College, Bachelor of Science, Accounting and Business Management. CUNY Graduate School and University Center, M...

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in Seattle, MCAT Tutors in San Diego, ACT Tutors in Chicago, Reading Tutors in New York City, English Tutors in Los Angeles, Computer Science Tutors in San Diego, Physics Tutors in Boston, GMAT Tutors in San Francisco-Bay Area, MCAT Tutors in Boston, Physics Tutors in New York City

Popular Courses & Classes

ACT Courses & Classes in Miami, SSAT Courses & Classes in Miami, GRE Courses & Classes in Phoenix, LSAT Courses & Classes in Denver, GMAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Washington DC, MCAT Courses & Classes in Phoenix, SSAT Courses & Classes in Atlanta, GMAT Courses & Classes in Seattle, Spanish Courses & Classes in Boston

Popular Test Prep

SAT Test Prep in Seattle, GRE Test Prep in Chicago, SAT Test Prep in Chicago, SSAT Test Prep in Dallas Fort Worth, ACT Test Prep in Chicago, ACT Test Prep in Washington DC, MCAT Test Prep in Los Angeles, GMAT Test Prep in Seattle, ACT Test Prep in Miami, MCAT 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

Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #12 : Factoring Polynomials

Example Question #3 : Factoring Polynomials

Example Question #13 : Factoring Polynomials

Example Question #14 : Factoring Polynomials

Example Question #15 : Factoring Polynomials

Example Question #21 : Factoring Polynomials

Example Question #22 : Factoring Polynomials

Example Question #23 : Factoring Polynomials

Example Question #24 : Factoring Polynomials

Example Question #25 : Factoring Polynomials

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: