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 创建测试&抽认卡

All GED Math Resources

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

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 … 16 17 Next →

Example Question #21 :Algebra

Simplify completely:

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

Possible Answers:

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

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

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

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

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 #22 :Algebra

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

Possible Answers:

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

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

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

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

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 #21 :Single Variable Algebra

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

Possible Answers:

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

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

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

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

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 #24 :Algebra

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 #21 :Single Variable Algebra

Simplify:

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

Possible Answers:

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

$9}{t^{3}$

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

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

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 #26 :Algebra

Factor completely:

$x^{3} + 121x$

Possible Answers:

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

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

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

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

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 #27 :Algebra

Factor completely:

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

Possible Answers:

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

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

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

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

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 #28 :Algebra

Factor completely:

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

Possible Answers:

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

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

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

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

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

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 #29 :Algebra

Factor completely:

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

Possible Answers:

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

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

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

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

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 #21 :Algebra

Factor completely:

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

Possible Answers:

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

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

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

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

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

← Previous 1 2 3 4 5 6 7 8 9 … 16 17 Next →

View Tutors

Joshua
Certified Tutor

Williams College, Bachelor in Arts, Chemistry.

View Tutors

Dale
Certified Tutor

View Tutors

Richard
Certified Tutor

American University, Bachelor in Arts, International Relations.

All GED Math Resources

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

Popular Subjects

Statistics Tutors in Washington DC,Math Tutors in San Diego,Chemistry Tutors in San Francisco-Bay Area,Chemistry Tutors in San Diego,Statistics Tutors in San Francisco-Bay Area,MCAT Tutors in Chicago,GRE Tutors in Los Angeles,SAT Tutors in Seattle,Physics Tutors in Boston,Reading Tutors in New York City

Popular Courses & Classes

LSAT Courses & Classes in Boston,GRE Courses & Classes in Philadelphia,Spanish Courses & Classes in Washington DC,GMAT Courses & Classes in Boston,ISEE Courses & Classes in Miami,MCAT Courses & Classes in Miami,GRE Courses & Classes in New York City,ISEE Courses & Classes in Seattle,MCAT Courses & Classes in Seattle,MCAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

SAT Test Prep in Phoenix,LSAT Test Prep in Boston,GRE Test Prep in San Francisco-Bay Area,SAT Test Prep in Los Angeles,LSAT Test Prep in Houston,ISEE Test Prep in San Francisco-Bay Area,ACT Test Prep in Dallas Fort Worth,GRE Test Prep in New York City,ISEE Test Prep in Boston,SAT 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.

哟ur 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:

哟u must include the following:

copyrigh的物理或电子签名t 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.

把你的投诉我们指定的代理:

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.

我承认可能有不利的法律上的缺点equences 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 #21 :Algebra

Example Question #22 :Algebra

Example Question #21 :Single Variable Algebra

Example Question #24 :Algebra

Example Question #21 :Single Variable Algebra

Example Question #26 :Algebra

Example Question #27 :Algebra

Example Question #28 :Algebra

Example Question #29 :Algebra

Example Question #21 :Algebra

All GED Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Find the Best Tutors

Email address:
哟ur name:
Feedback: