Call Now to Set Up Tutoring:

(888) 888-0446

GED Math : GED Math

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 #16 : Simplifying, Distributing, And Factoring

Factor completely:

$9t^{2} - 81t$

Possible Answers:

$9 \left ( t+3\right )(t-3)$

9(t-3)(t+27)

$9 (t-3)^{2}$

9t (t-9)

Correct answer:

9t (t-9)

Explanation:

The common factor of the terms $9t^{2}$ and 81t can be found as follows:

GCF (9,81) = 9 , and the lesser of the two powers of is ; therefore, $GCF (9t^{2},81t) = 9t$ , their product. Distribute this out:

$9t^{2} - 81t$

$= 9t \cdot t - 9t \cdot 9$

$= 9t \left (t - 9 \right )$

This is as far as we can go with the factoring.

Report an Error

Example Question #12 : Algebra

Factor completely:

30xt + 15x -22t - 11

Possible Answers:

$\left (6x+11 \right ) \left ( 5t - 1 \right )$

$\left (15x + 11 \right ) \left ( 2t -1 \right )$

$\left (6x- 11 \right ) \left ( 5t + 1 \right )$

$\left (15x - 11 \right ) \left ( 2t + 1 \right )$

Correct answer:

$\left (15x - 11 \right ) \left ( 2t + 1 \right )$

Explanation:

Use the grouping technique - group the terms into pairs, then factor out the greatest common factor of each pair.

30xt + 15x -22t - 11

$= \left (30xt + 15x \right ) -\left (22t + 11 \right )$

$= \left (15x \cdot 2t + 15x \cdot 1 \right ) -\left ( 11 \cdot 2t + 11 \cdot 1 \right )$

$= 15x \left ( 2t + 1 \right ) - 11 \left ( 2t + 1 \right )$

$= \left (15x - 11 \right ) \left ( 2t + 1 \right )$

Report an Error

Example Question #571 : Ged Math

Factor completely:

$2x^{2} + 21x - 50$

Possible Answers:

$\left (2x- 1\right ) \left (x+25 \right )$

$2 \left (x+5 \right ) \left (x-5 \right )$

$\left (2x+ 5\right ) \left (x-2 \right )$

$\left (2x+ 25 \right ) \left (x-2 \right )$

Correct answer:

$\left (2x+ 25 \right ) \left (x-2 \right )$

Explanation:

A polynomial of the form $Ax^{2} + Bx + C$ can be factored by first splitting the term into two terms whose coefficients add up to and have product , then factoring out by the grouping technique.

We are looking for two integers whose sum is B = 21 and whose product is AC = 2 (-50) = -100 . Through some trial and error, we can see that the integers are $\left \{ 25, -4 \right \}$ , so:

$2x^{2} + 21x - 50$

$=2x^{2} - 4x + 25x - 50$

$=\left (2x^{2} - 4x \right )+\left ( 25x - 50 \right )$

$=\left (2x \cdot x - 2x \cdot 2 \right )+\left ( 25 \cdot x - 25 \cdot 2 \right )$

$= 2x \left (x-2 \right )+ 25 \left (x-2 \right )$

$= \left (2x+ 25 \right ) \left (x-2 \right )$

Report an Error

Example Question #15 : Simplifying, Distributing, And Factoring

Factor completely:

$4x ^{3}y - 100xy$

Possible Answers:

$2x y \left ( 2x + 5 \right ) \left ( x - 10 \right )$

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

$2x y \left ( 2x - 5 \right ) \left ( x + 10 \right )$

$4x y \left ( x + 5 \right ) \left ( x - 5 \right )$

Correct answer:

$4x y \left ( x + 5 \right ) \left ( x - 5 \right )$

Explanation:

First, factor out the greatest common factor of the terms, which is 4x y :

$4x ^{3}y - 100xy$

$= 4x y \cdot x^{2} - 4x y \cdot 25$

$= 4x y \left ( x^{2} - 25 \right )$

$x^{2} - 25$ is the difference of squares, so we can factor further:

$4x y \left ( x^{2} - 25 \right )$

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

$4x y \left ( x + 5 \right ) \left ( x - 5 \right )$

Report an Error

Example Question #12 : Algebra

Simplify:

7 (2x + 8)- 5 (7x - 3)

Possible Answers:

-21x+ 41

-49x+ 71

-49x+ 41

-21x+ 71

Correct answer:

-21x+ 71

Explanation:

7 (2x + 8)- 5 (7x - 3)

$= 7 \cdot 2x +7 \cdot 8- 5 \cdot 7x + 5 \cdot 3$

= 14x +56- 35x + 15

= 14x- 35x +56+ 15

$= \left (14 - 35 \right )x +\left (56+ 15 \right )$

= -21x+ 71

Report an Error

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 #571 : Ged Math

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

Possible Answers:

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

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

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

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

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 #571 : Ged Math

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

Possible Answers:

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

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

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

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

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 #572 : Ged Math

Factor completely:

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

Possible Answers:

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

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

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

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

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 #571 : Ged Math

Simplify:

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

Possible Answers:

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

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

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

$9}{t^{3}$

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

View Tutors

Aswathi
Certified Tutor

Kannur University , Master's/Graduate, English Language and Literature .

View Tutors

Lori
Certified Tutor

Iowa State University, Bachelor of Science, Aerospace Engineering. Rockhurst University, Master of Science, Physical Therapy.

View Tutors

Chang Keun
Certified Tutor

University of Waterloo, Bachelor in Arts, Electrical Engineering.

All GED Math Resources

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

Popular Subjects

Biology Tutors in Seattle, SSAT Tutors in New York City, Physics Tutors in Chicago, ACT Tutors in Washington DC, GRE Tutors in New York City, Biology Tutors in Atlanta, Statistics Tutors in Seattle, English Tutors in New York City, Computer Science Tutors in Boston, Spanish Tutors in San Francisco-Bay Area

Popular Courses & Classes

GMAT Courses & Classes in Denver, GRE Courses & Classes in Miami, MCAT Courses & Classes in Boston, LSAT Courses & Classes in New York City, LSAT Courses & Classes in Philadelphia, GRE Courses & Classes in Denver, SAT Courses & Classes in Houston, LSAT Courses & Classes in Washington DC, ISEE Courses & Classes in Seattle, ACT Courses & Classes in Miami

Popular Test Prep

MCAT Test Prep in Atlanta, GRE Test Prep in Washington DC, GMAT Test Prep in Miami, LSAT Test Prep in Houston, ISEE Test Prep in Chicago, LSAT Test Prep in Los Angeles, ACT Test Prep in Atlanta, SSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Philadelphia, LSAT Test Prep in Miami

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 : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #16 : Simplifying, Distributing, And Factoring

Example Question #12 : Algebra

Example Question #571 : Ged Math

Example Question #15 : Simplifying, Distributing, And Factoring

Example Question #12 : Algebra

Example Question #21 : Algebra

Example Question #571 : Ged Math

Example Question #571 : Ged Math

Example Question #572 : Ged Math

Example Question #571 : Ged Math

All GED Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: