Call Now to Set Up Tutoring:

(888) 888-0446

GED Math : Single-Variable Algebra

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 #11 : Simplifying, Distributing, And Factoring

Express 286 in base five.

Possible Answers:

$2201_{\textrm{five}}$

$2121_{\textrm{five}}$

$2101_{\textrm{five}}$

$2221_{\textrm{five}}$

Correct answer:

$2121_{\textrm{five}}$

Explanation:

To convert a base ten number to base five, divide the number by five, with the remainder being the digit in the units place; continue, dividing each successive quotient by five and putting the remainder in the next position to the left until the final quotient is less than five.

$286\div 5 = 57 \textrm{ R }\underline{1}$ - 1 is the last digit.

$57 \div 5 = 11 \textrm{ R }\underline{2}$ - 2 is the second-to-last digit.

$11 \div 5 = \underline{2} \textrm{ R }\underline{1}$ - 1 is the third-to-last digit; 2 is the first digit.

286 is equal to $2121_{\textrm{five}}$ .

Report an Error

Example Question #12 : Simplifying, Distributing, And Factoring

Simplify the following: 2x^2 - 3y - 4x^2 + 3y^2 - 3x

Possible Answers:

2x^2 - 3x - 3y

-5x^2 - 3x

2x^2 + 3y^2 - 3x + 3y

-2x^2 + 3y^2 - 3x - 3y

-2x^2 - 3y^2 - 3x - 3y

Correct answer:

-2x^2 + 3y^2 - 3x - 3y

Explanation:

Group all like terms by their order:

2x^2 - 3y - 4x^2 + 3y^2 - 3x

2x^2 - 4x^2 + 3y^2 - 3x- 3y

Simplify:

-2x^2 + 3y^2 - 3x - 3y

Report an Error

Example Question #13 : Simplifying, Distributing, And Factoring

Simplify the following: -(2-x)(6-x)

Possible Answers:

-x^2 +4x-12

-x^2 +8x-12

-x^2 -4x-12

-x^2 +8x+12

-x^2 -8x-12

Correct answer:

-x^2 +8x-12

Explanation:

This can be solved using the FOIL method. The steps are shown below.

-(2-x)(6-x)

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

-(12-2x-6x+x^2)

-(12-8x+x^2)

-12+8x-x^2

Therefore, after reordering, the answer is: -x^2+8x-12

Report an Error

Example Question #11 : Single Variable Algebra

Simplify:

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

Possible Answers:

$\frac{1}{4x^{8}}$

$\frac{x^{8}}{4}$

$\frac{x^{8}}{256}$

$\frac{1}{256x^{8}}$

Correct answer:

$\frac{x^{8}}{4}$

Explanation:

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

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

$=\left ( \frac{x^{4}}{2} \right )^{2}$

$= \frac{\left (x^{4}\right )^{2}}{2^{2}}$

$= \frac{ x^{4 \cdot 2} }{2^{2}}$

$= \frac{ x^{8} }{4}$

Report an Error

Example Question #15 : Simplifying, Distributing, And Factoring

Factor completely:

$8t^{3} -56t^{2} +3t -21$

Possible Answers:

$(8t^{2}+7) (t-3)$

$(8t^{2}-7) (t+3)$

$(8t^{2}+3) (t-7)$

$(8t^{2}-3) (t+7)$

Correct answer:

$(8t^{2}+3) (t-7)$

Explanation:

Use the grouping technique, then distribute out the greatest common factor of each group as follows:

$8t^{3} -56t^{2} +3t -21$

$=\left ( 8t^{3} -56t^{2} \right ) +\left (3t -21 \right )$

$=\left ( 8t^{2} \cdot t -8t^{2} \cdot 7 \right ) +\left (3 \cdot t -3 \cdot 7\right )$

$=8t^{2} \left ( t - 7 \right ) + 3\left ( t - 7 \right )$

$=\left (8t^{2} + 3 \right ) \left ( t - 7 \right )$

Report an Error

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:

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

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

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

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

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 #11 : Algebra

Factor completely:

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

Possible Answers:

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

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

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

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

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

View Tutors

Judith
Certified Tutor

Ohio University-Main Campus, Bachelor in Arts, Global Studies.

View Tutors

Mark
Certified Tutor

Murray State University, Bachelor of Science, Mathematics.

View Tutors

Alex
Certified Tutor

Vanderbilt University, Bachelor of Science, Psychology. Boston University, Master of Science, Speech-Language Pathology.

All GED Math Resources

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

Popular Subjects

Computer Science Tutors in Seattle, MCAT Tutors in New York City, Spanish Tutors in Houston, ACT Tutors in Houston, ACT Tutors in Phoenix, ISEE Tutors in Phoenix, GMAT Tutors in Miami, French Tutors in San Francisco-Bay Area, Physics Tutors in Boston, Biology Tutors in San Francisco-Bay Area

Popular Courses & Classes

MCAT Courses & Classes in Boston, GRE Courses & Classes in Phoenix, GRE Courses & Classes in Denver, Spanish Courses & Classes in New York City, SSAT Courses & Classes in Denver, ISEE Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Houston, ACT Courses & Classes in Houston, MCAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Chicago

Popular Test Prep

SAT Test Prep in Phoenix, SAT Test Prep in Boston, SAT Test Prep in Chicago, MCAT Test Prep in Denver, LSAT Test Prep in Philadelphia, GRE Test Prep in New York City, ACT Test Prep in Washington DC, MCAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Seattle, SSAT Test Prep in Atlanta

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 : Single-Variable Algebra

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #11 : Simplifying, Distributing, And Factoring

Example Question #12 : Simplifying, Distributing, And Factoring

Example Question #13 : Simplifying, Distributing, And Factoring

Example Question #11 : Single Variable Algebra

Example Question #15 : Simplifying, Distributing, And Factoring

Example Question #16 : Simplifying, Distributing, And Factoring

Example Question #12 : Algebra

Example Question #11 : Algebra

Example Question #15 : Simplifying, Distributing, And Factoring

Example Question #12 : Algebra

All GED Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: