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 #1 : Algebra

Multiply:

$\small -x(4x+2)=$

Possible Answers:

$\small -4x^2-2x$

$\small 4x^2-2x$

$\small -4x^2+2x$

$\small 4x^2+2x$

Correct answer:

$\small -4x^2-2x$

Explanation:

$\small -x(4x+2)=(-x)(4x)+(-x)(2)=-4x^2+(-2x)=-4x^2-2x$

Report an Error

Example Question #1 : Algebra

Factor:

$\small x^2+5x+4$

Possible Answers:

$\small (x-4)(x-1)$

$\small (x+5)(x-1)$

$\small (x-5)(x+1)$

$\small (x+4)(x+1)$

Correct answer:

$\small (x+4)(x+1)$

Explanation:

$\small x^2+5x+4=(x+a)(x+b)$

where

$\small a+b=5\ and\ ab=4$

The numbers $\small 4$ and $\small 1$ fit those criteria. Therefore,

$\small x^2+5x+4=(x+1)(x+4)$

You can double check the answer using the FOIL method

Report an Error

Example Question #1 : Algebra

Which of the following is not a prime factor of $y^{4}- 81$ ?

Possible Answers:

$y^{2}+9$

$y^{2}-9$

y - 3

y + 3

Correct answer:

$y^{2}-9$

Explanation:

Factor $y^{4}- 81$ all the way to its prime factorization.

$y^{4}- 81$ can be factored as the difference of two perfect square terms as follows:

$y^{4}- 81$

$=\left ( y^{2} \right )^{2} - 9^{2}$

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

$y^{2} + 9$ is a factor, and, as the sum of squares, it is a prime. $y^{2} - 9$ is also a factor, but it is not a prime factor - it can be factored as the difference of two perfect square terms. We continue:

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

$=\left ( y^{2} + 9 \right )\left ( y^{2} - 3^{2} \right )$

$=\left ( y^{2} + 9 \right )\left (y+3 \right )\left ( y-3\right )$

Therefore, all of the given polynomials are factors of $y^{4}- 81$ , but $y^{2} - 9$ is the correct choice, as it is not a prime factor.

Report an Error

Example Question #1 : Algebra

Which of the following is a prime factor of $n^{4} + 30n^{2} +225$ ?

Possible Answers:

$n^{2}+9$

$n^{2}+25$

$n^{2}+15$

$n^{2}+75$

Correct answer:

$n^{2}+15$

Explanation:

$n^{4} + 30n^{2} +225$ can be seen to fit the pattern

$A ^{2} + 2AB + B^{2}$ :

$n^{4} + 30n^{2} +225 = \left (n^{2} \right ) ^{2}+ 2 \cdot n^{2} \cdot 15 + 15 ^{2}$

where $A = n^{2} , B = 15$

$A ^{2}+2AB + B^{2}$ can be factored as $(A+B ) ^{2}$ , so

$n^{4} + 30n^{2} +225 = \left (n^{2} \right ) ^{2}+ 2 \cdot n^{2} \cdot 15 + 15 ^{2} = (n^{2}+15)^{2}$ .

$n^{2}+15$ does not fit into any factorization pattern, so it is prime, and the above is the complete factorization of the polynomial. Therefore, $n^{2}+15$ is the correct choice.

Report an Error

Example Question #2 : Algebra

Divide:

$\left ( 12 x ^{5} + 9x^{3}+ 6x^{2}+36 x \right ) \div 6x$

Possible Answers:

$2x ^{4} +3x ^{2} + 6$

$6x ^{4} + 3x ^{2} + 30$

$2x ^{4} + \frac{ 3 }{2 }x ^{2} + x+ 6$

$6x ^{4} + 3x ^{2} +x + 30$

Correct answer:

$2x ^{4} + \frac{ 3 }{2 }x ^{2} + x+ 6$

Explanation:

Divide termwise:

$\left ( 12 x ^{5} + 9x^{3}+ 6x^{2}+36 x \right ) \div 6x$

$= \frac{ 12 x ^{5} + 9x^{3}+ 6x^{2}+36 x }{6x}$

$= \frac{ 12 x ^{5} }{6x} + \frac{ 9x^{3} }{6x} + \frac{ 6x^{2} }{6x}+ \frac{ 36 x }{6x}$

$= \frac{ 12 }{6} x ^{5-1} + \frac{ 9 }{6 }x ^{3-1} + \frac{ 6 }{6}x^{2-1}+ \frac{ 36 }{6 }$

$=2x ^{4} + \frac{ 3 }{2 }x ^{2} + x+ 6$

Report an Error

Example Question #5 : Algebra

Multiply:

$\left (100Y^{2}+ 110Y + 121 \right )(10Y-11)$

Possible Answers:

$1,000Y^{3}- 1,100Y^{2}+1,210Y - 1,331$

$1,000Y^{3}+ 1,100Y^{2}-1,210Y - 1,331$

$1,000Y^{3}- 3,300Y^{2}+3,630Y - 1,331$

$1,000Y^{3}- 1,331$

Correct answer:

$1,000Y^{3}- 1,331$

Explanation:

$\left (100Y^{2}+ 110Y + 121 \right )(10Y-11)$

$=\left [\left (10Y \right) ^{2}+ 10Y \cdot 11 + 11^{2} \right] (10Y-11)$

This product fits the difference of cubes pattern, where A = 10Y, B = 11 :

$(A^{2}+AB +B^{2})(A-B) = A^{3}-B^{3}$

$\left [\left (10Y \right) ^{2}+ 10Y \cdot 11 + 11^{2} \right] (10Y-11)$

$= \left ( 10Y\right )^{3} -11^{3} = 1,000Y^{3}-1,331$

Report an Error

Example Question #6 : Algebra

Give the value of that makes the polynomial $121x^{2}- Nx + 49$ the square of a linear binomial.

Possible Answers:

N = 231

N = 198

N = 154

N = 77

Correct answer:

N = 154

Explanation:

A quadratic trinomial is a perfect square if and only if takes the form

$A^{2} \pm 2AB + B^{2}$ for some values of and .

$121x^{2}- Nx + 49= (11x)^{2} - Nx + 7^{2}$ , so

A = 11x and B = 7 .

For $121x^{2}- Nx + 49$ to be a perfect square, it must hold that

$Nx = 2AB = 2 \cdot 11x \cdot 7 = 154x$ ,

so N = 154 . This is the correct choice.

Report an Error

Example Question #4 : Algebra

Which of the following is a factor of the polynomial $x^{4}-13x^{2}+ 36$ ?

Possible Answers:

x-9

x - 4

x-2

x-1

Correct answer:

x-2

Explanation:

Perhaps the easiest way to identify the factor is to take advantage of the factor theorem, which states that x-a is a factor of polynomial P(x) if and only if P(a)= 0 . We substitute 1, 2, 4, and 9 for in the polynomial to identify the factor.

x=1 :

$1^{4}-13 \cdot 1^{2}+ 36$

= 1 - 13 + 36

= 24

x=2 :

$2^{4}-13 \cdot 2^{2}+ 36$

$= 16- 13 \cdot 4 + 36$

= 16 -52 + 36

= 0

x =4 :

$4^{4}-13 \cdot 4^{2}+ 36$

$= 256- 13 \cdot 16 + 36$

= 256 -208 +36

= 84

x=9 :

$9^{4}-13 \cdot 9^{2}+ 36$

$= 6,561- 13 \cdot 81 + 36$

= 6,561- 1,053+ 36

= 5,544

Only x = 2 makes the polynomial equal to 0, so among the choices, only x-2 is a factor.

Report an Error

Example Question #5 : Algebra

Which of the following is a prime factor of $x^{6} +1$ ?

Possible Answers:

$x^{2}+1$

$x^{2}-x+1$

$x^{2}+x+1$

x+1

Correct answer:

$x^{2}+1$

Explanation:

$x^{6} +1$ is the sum of two cubes:

$x^{6} +1 =\left ( x^{2} \right ) ^{3}+1^{3}$

As such, it can be factored using the pattern

$A^{3}+ B^{3}= (A+B)(A^{2}-AB+B^{2})$

where $A = x^{2}, B = 1$ ;

$x^{6} +1 =\left ( x^{2} \right ) ^{3}+1^{3}$

$= (x^{2}+1)((x^{2})^{2}-x^{2} \cdot 1 + 1^{2})$

$= (x^{2}+1)(x^{4}-x^{2} + 1)$

The first factor,as the sum of squares, is a prime.

We try to factor the second by noting that it is "quadratic-style" based on $x^{2}$ . and can be written as

$= (x^{2})^{2}-x^{2} + 1$ ;

we seek to factor it as $(x^{2}+\; \; \; )(x^{2}+\; \; \; )$

We want a pair of integers whose product is 1 and whose sum is . These integers do not exist, so $x^{4}-x^{2} + 1$ is a prime.

$(x^{2}+1)(x^{4}-x^{2} + 1)$ is the prime factorization and the correct response is $x^{2}+1$ .

Report an Error

Example Question #7 : Algebra

Which of the following is a factor of the polynomial $x^{6} - 66x^{3} + 128$

Possible Answers:

x-4

x+4

x-2

x+2

Correct answer:

x-4

Explanation:

Perhaps the easiest way to identify the factor is to take advantage of the factor theorem, which states that x-a is a factor of polynomial P(x) if and only if P(a)= 0 . We substitute $\pm2$ and $\pm 4$ for in the polynomial to identify the factor.

x = 2 :

$x^{6} - 66x^{3} + 128$

$2^{6} - 66 \cdot 2^{3} + 128$

$= 64 - 66 \cdot 8 + 128$

= 64 - 528 + 128

= -336

x = -2 :

$x^{6} - 66x^{3} + 128$

$\left (-2 \right )^{6} - 66 \cdot \left (-2 \right )^{3} + 128$

$= 64 - 66 \cdot\left ( -8 \right )+ 128$

= 64 + 528 + 128

= 720

x = 4 :

$x^{6} - 66x^{3} + 128$

$4^{6} - 66 \cdot 4^{3} + 128$

$= 4,096- 66 \cdot 64 + 128$

= 4,096- 4,224 + 128

= 0

x = -4 :

$x^{6} - 66x^{3} + 128$

$\left (-4 \right )^{6} - 66 \cdot \left (-4 \right )^{3} + 128$

$= 4,096- 66 \cdot\left ( -64 \right )+ 128$

= 4,096+4,224 + 128

= 8,448

Only x = 4 makes the polynomial equal to 0, so of the four choices, only x - 4 is a factor of the polynomial.

Report an Error

View Tutors

Blossom
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Computer Science.

View Tutors

Abhisek
Certified Tutor

University of Florida, Bachelor of Engineering, Computer Science.

View Tutors

Alyce
Certified Tutor

The University of Alabama, Master of Arts, German.

All GED Math Resources

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

Popular Subjects

GMAT Tutors in Atlanta, Reading Tutors in Miami, Chemistry Tutors in Los Angeles, MCAT Tutors in Miami, Statistics Tutors in Dallas Fort Worth, GRE Tutors in Houston, MCAT Tutors in Boston, GRE Tutors in Miami, ISEE Tutors in Houston, MCAT Tutors in Atlanta

Popular Courses & Classes

GRE Courses & Classes in Seattle, LSAT Courses & Classes in Miami, SAT Courses & Classes in Seattle, ISEE Courses & Classes in Seattle, GMAT Courses & Classes in San Diego, SAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Phoenix, GRE Courses & Classes in New York City, GRE Courses & Classes in Phoenix, ISEE Courses & Classes in Philadelphia

Popular Test Prep

LSAT Test Prep in New York City, SSAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Philadelphia, MCAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Los Angeles, LSAT Test Prep in Denver, GRE Test Prep in Chicago, GMAT Test Prep in Atlanta, MCAT Test Prep in Boston, LSAT Test Prep in Seattle

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 #1 : Algebra

Example Question #1 : Algebra

Example Question #1 : Algebra

Example Question #1 : Algebra

Example Question #2 : Algebra

Example Question #5 : Algebra

Example Question #6 : Algebra

Example Question #4 : Algebra

Example Question #5 : Algebra

Example Question #7 : Algebra

All GED Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: