Call Now to Set Up Tutoring:

(888) 888-0446

GED Math : Simplifying, Distributing, and Factoring

Study concepts, example questions & explanations for GED Math

Create An Account

All GED Math Resources

4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : Algebra

Simplify completely:

$\frac{3xy \cdot 7xy}{12y^{3}}$

Possible Answers:

$\frac{7 x }{4y^{2} }$

$\frac{7 x^{2}y }{4 }$

$\frac{7 x^{2} }{4y^{2} }$

$\frac{7 x^{2} }{4y }$

Correct answer:

$\frac{7 x^{2} }{4y }$

Explanation:

$\frac{3xy \cdot 7xy}{12y^{3}}$

$= \frac{3 \cdot 7 \cdot x \cdot x \cdot y \cdot y}{12y^{3}}$

$= \frac{21 x^{2} y^{2} }{12y^{3}}$

$= \frac{21 x^{2} }{12y^{3-2}}$

$= \frac{21 x^{2} }{12y }$

$= \frac{21 x^{2} \div 3 }{12y \div 3}$

$= \frac{7 x^{2} }{4y }$

Report an Error

Example Question #21 : Algebra

Subtract $x^{2} - 5$ from $8x ^{2} -7x + 4$ .

Possible Answers:

$7x ^{2} -7x +9$

$8x ^{2} -8x -1$

$8x ^{2} -8x + 9$

$7x ^{2} -7x -1$

Correct answer:

$7x ^{2} -7x +9$

Explanation:

$(8x ^{2} -7x + 4) -(x^{2} - 5)$

$= 8x ^{2} -7x + 4 -x^{2} + 5$

$= 8x ^{2} -1x^{2} -7x + 4 + 5$

$=\left ( 8-1 \right )x ^{2} -7x +\left ( 4 + 5 \right )$

$=7x ^{2} -7x +9$

Report an Error

Example Question #22 : Algebra

Add $x^{2} - 5$ to $8x ^{2} -7x + 4$ .

Possible Answers:

$8x ^{2} -6x -1$

$8x ^{2} -6x -9$

$9x ^{2} -7x -1$

$9x ^{2} -7x -9$

Correct answer:

$9x ^{2} -7x -1$

Explanation:

$(8x ^{2} -7x + 4) +(x^{2} - 5)$

$=8x ^{2} + x^{2} -7x + 4 - 5$

$=\left ( 8+1 \right ) x ^{2} -7x +\left ( 4 - 5 \right )$

$=9x ^{2} -7x -1$

Report an Error

Example Question #23 : Algebra

Factor completely:

$5y^{3}- 20y^{2}- 105y$

Possible Answers:

5y (y-7)(y + 3)

5y (y-21)(y + 1)

5y (y-3)(y + 7)

5y (y-1)(y +2 1)

Correct answer:

5y (y-7)(y + 3)

Explanation:

First, factor out the greatest common factor of the terms, which is :

$5y^{3}- 20y^{2}- 105y$

$= 5y \cdot y^{2}- 5y \cdot 4y- 5y \cdot 21$

$= 5y \left (y^{2}- 4y- 21 \right )$

The quadratic trinomial can be factored as (x+A)(x+ B) where A = -21 and A + B = -4 ; by trial and error we find that the numbers chosen are A = -7, B = 3 , so

$5y \left (y^{2}- 4y- 21 \right )$

= 5y (y-7)(y + 3)

Report an Error

Example Question #21 : Simplifying, Distributing, And Factoring

Simplify:

$\left (\frac{3}{t} \right )^{3}$

Possible Answers:

$9}{t^{3}$

$\frac{27}{t^{3}}$

$\frac{t^{3}}{27}$

$\frac{9}{t^{3}}$

Correct answer:

$\frac{27}{t^{3}}$

Explanation:

Apply the power of a quotient rule:

$\left (\frac{3}{t} \right )^{3} = \frac{3^{3}}{t^{3}} = \frac{27}{t^{3}}$

Report an Error

Example Question #22 : Algebra

Factor completely:

$x^{3} + 121x$

Possible Answers:

$x^{2} (x+ 121)$

$\left (x ^{2} + 11 \right ) (x+ 11)$

$x (x^{2}+ 121)$

$x \left ( x + 11\right )^{2}$

Correct answer:

$x (x^{2}+ 121)$

Explanation:

is a common factor of both terms, so factor it out:

$x^{3} + 121x$

$= x \cdot x ^{2} +x \cdot 121$

$= x \left ( x ^{2} + 121 \right )$

$= x ^{2} + 121$ cannot be factored, so this is the complete factorization.

Report an Error

Example Question #22 : Single Variable Algebra

Factor completely:

$12x^{2} + 19x + 4$

Possible Answers:

$4 \left (3x + 1 \right )\left (x+1 \right )$

$2 \left (3x + 2 \right )\left (2x+ 1 \right )$

$\left (3x + 4 \right )\left (4x+ 1 \right )$

$2\left (x + 2 \right )\left (6x+ 1 \right )$

Correct answer:

$\left (3x + 4 \right )\left (4x+ 1 \right )$

Explanation:

First, we find two integers whose sum is 19 and whose product is $12 \times 4 = 48$ . Through trial and error we find these integers are 3 and 16. We use these numbers to split the middle term, then we factor using the grouping method:

$12x^{2} + 19x + 4$

$= 12x^{2}+ 3x + 16x + 4$

$= \left (12x^{2}+ 3x \right )+ \left (16x + 4 \right )$

$= \left (3x \cdot 4x+ 3x \cdot 1 \right )+ \left (4 \cdot 4x + 4 \cdot 1 \right )$

$= 3x \left (4x+ 1 \right )+ 4\left (4x+ 1 \right )$

$= \left (3x + 4 \right )\left (4x+ 1 \right )$

Report an Error

Example Question #581 : Ged Math

Factor completely:

$5x ^{3}+ 25x^{2} - 7x - 35$

Possible Answers:

$\left (5x ^{2} +1 \right ) \left ( x - 35 \right )$

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

$5 \left (x ^{2} +1 \right ) \left ( x - 7 \right )$

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

$\left (5x ^{2} - 1 \right ) \left ( x + 35 \right )$

Correct answer:

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

Explanation:

Factor by grouping as follows:

$5x ^{3}+ 25x^{2} - 7x - 35$

$=\left (5x ^{3}+ 25x^{2} \right )- \left (7x + 35 \right )$

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

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

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

Report an Error

Example Question #24 : Algebra

Factor completely:

$x ^{3} + 7x ^{2} - 9x - 63$

Possible Answers:

$\left (x^{2}+ 7 \right )\left ( x-9\right )$

$\left (x^{2}+ 9\right )\left ( x-7\right )$

$\left ( x + 3 \right )\left ( x - 3 \right ) \left ( x + 7 \right )$

$\left (x^{2}-7 \right )\left ( x+ 9 \right )$

Correct answer:

$\left ( x + 3 \right )\left ( x - 3 \right ) \left ( x + 7 \right )$

Explanation:

Factor by grouping as follows:

$x ^{3} + 7x ^{2} - 9x - 63$

$= \left (x ^{3} + 7x ^{2} \right )- \left (9x + 63 \right )$

$= \left (x ^{2} \cdot x + x ^{2} \cdot 7 \right )- \left (9 \cdot x + 9 \cdot 7\right )$

$= x ^{2} \left ( x + 7 \right )- 9 \left ( x + 7\right )$

$=\left ( x ^{2}- 9 \right ) \left ( x + 7 \right )$

The first factor is the difference of squares, so further factoring can be done:

$=\left ( x ^{2}- 3 ^{2} \right ) \left ( x + 7 \right )$

$=\left ( x + 3 \right )\left ( x - 3 \right ) \left ( x + 7 \right )$

Report an Error

Example Question #25 : Algebra

Factor completely:

$49x^{2} - 70x+ 25$

Possible Answers:

$(7x - 5)^{2}$

(7x + 1)(7x - 25)

(7x+5)(7x - 5)

(7x - 1)(7x - 25)

Correct answer:

$(7x - 5)^{2}$

Explanation:

The polynomial fits the perfect square pattern:

$49x^{2} - 70x+ 25$

$\left (7x \right )^{2} - 2 \cdot 7x \cdot 5 + 5^{2}$

This can be factored using the pattern

$A^{2} - 2AB + B ^{2} = (A+B)^{2}$

with A = 7x, B = 5 :

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

Report an Error

View Tutors

Donald
Certified Tutor

Cleveland State University, Bachelor of Science, Chemistry. University of Southern California, Doctor of Philosophy, Organic ...

View Tutors

Victoria
Certified Tutor

Norte Dame de Namur University, Bachelor in Arts, Sociology. University of San Francisco, Master of Arts, Organizational Lead...

View Tutors

Shweta
Certified Tutor

All India Management Association , Master's/Graduate, Human Resource Management . Indian Law Institute , Master's/Graduate, C...

All GED Math Resources

4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Washington DC, ACT Tutors in New York City, SAT Tutors in Dallas Fort Worth, SSAT Tutors in San Diego, Reading Tutors in Phoenix, Algebra Tutors in New York City, SAT Tutors in San Francisco-Bay Area, Algebra Tutors in Phoenix, Computer Science Tutors in Philadelphia, Math Tutors in Philadelphia

Popular Courses & Classes

GRE Courses & Classes in San Diego, Spanish Courses & Classes in Philadelphia, Spanish Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Phoenix, LSAT Courses & Classes in Atlanta, ISEE Courses & Classes in San Diego, SAT Courses & Classes in Washington DC, Spanish Courses & Classes in Washington DC, GMAT Courses & Classes in Houston, ISEE Courses & Classes in Denver

Popular Test Prep

ISEE Test Prep in Chicago, GRE Test Prep in San Diego, LSAT Test Prep in Boston, GRE Test Prep in Seattle, GRE Test Prep in New York City, SSAT Test Prep in Phoenix, MCAT Test Prep in San Diego, ACT Test Prep in Dallas Fort Worth, ACT Test Prep in San Diego, GRE Test Prep in San Francisco-Bay Area

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

GED Math : Simplifying, Distributing, and Factoring

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #21 : Algebra

Example Question #21 : Algebra

Example Question #22 : Algebra

Example Question #23 : Algebra

Example Question #21 : Simplifying, Distributing, And Factoring

Example Question #22 : Algebra

Example Question #22 : Single Variable Algebra

Example Question #581 : Ged Math

Example Question #24 : Algebra

Example Question #25 : Algebra

All GED Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: