Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Polynomials

If $f(x)=x^{3}-1$ and $g(x)=x^{2}+1$ , what is g(f(2)) ?

Possible Answers:

124

Correct answer:

Explanation:

g(f(2)) is a composite function where f(2) is plugged into g(x) :

$f(2)=(2)^{3}-1=8-1=7$

$g(7)=(7)^{2}+1=49+1=50$

Report an Error

Example Question #1 : Simplifying Polynomials

Simplify the following expression:

$3x^9y^4 \cdot (2y)^3$ .

Possible Answers:

11x^9y^7

$24x^9y^{12}$

24x^9y^7

18x^9y^6

Correct answer:

24x^9y^7

Explanation:

First, multiply out the second expression so that you get 8y^3 .

Then, multiply your like terms, taking care to remember that when multiplying terms that have the same base, you add the exponents. Thus, you get $24x^9y^{12}$ .

Report an Error

Example Question #1 : Polynomials

Simplify:

$\frac{13x^2y^5z^9}{169xy^5z^4}$

Possible Answers:

xz^5

xy^5

$\frac{x}{13}$

$\frac{xz^5}{13}$

$\frac{xz^5}{169}$

Correct answer:

$\frac{xz^5}{13}$

Explanation:

Focus on each pair of like terms. The y's completely cancel out, there is one left on top, and five z's left on the bottom.

$\frac{13}{169}$ reduces to $\frac{1}{13}$ .

Put that all together to get $\frac{xz^5}{13}$ .

Report an Error

Example Question #2 : Simplifying Polynomials

Simplify.

$x^{-6}x^3x^9$

Possible Answers:

$x^{12}$

x^6

$x^{-6}$

$x^{-12}$

Correct answer:

x^6

Explanation:

Put the negative exponent on the bottom so that you have $\frac{x^{12}}{x^{6}}$ which simplifies further to $x^{6}$ .

Report an Error

Example Question #3 : Simplifying Polynomials

Expand this expression:

(x-4) (2x+4)

Possible Answers:

2x - 4x - 16

2x^2 + 4x - 16

2x^2 - 4x - 16

2x^2 - 4x + 16

2x^2 + 4x + 16

Correct answer:

2x^2 - 4x - 16

Explanation:

Use the FOIL method (First, Outer, Inner, Last):

x * 2x = 2x^2

x * 4 = 4x

-4 * 2x = -8x

-4 * 4 = -16

Put all of these terms together:

2x^2 + 4x - 8x - 16

Combine like terms:

2x^2 - 4x - 16

Report an Error

Example Question #1 : Simplifying Polynomials

Simplify the following polynomial:

$ab^{-2}(a^2b+a^{-1}b^3-a^3b^{-1})$

Possible Answers:

$\frac{a^3}{b}+a-\frac{a^4}{b^3}$

$\frac{a^2}{b}+b-\frac{a^4}{b^3}$

$\frac{a^3}{b}+b-\frac{a^3}{b^4}$

$\frac{a^3}{b}+b-\frac{a^4}{b^3}$

$\frac{a^3}{b}+b^2-\frac{a^4}{b^3}$

Correct answer:

$\frac{a^3}{b}+b-\frac{a^4}{b^3}$

Explanation:

To simplify the polynomial, begin by multiplying the first binomial by every term within the parentheses:

$ab^{-2}(a^2b+a^{-1}b^3-a^3b^{-1})$

$aa^2b^{-2}b+aa^{-1}b^{-2}b^3-aa^3b^{-2}b^{-1}$

Now, combine like terms:

$a^3b^{-1}+b^1-a^4b^{-3}$

Convert the polynomial into fraction form:

$\frac{a^3}{b}+b-\frac{a^4}{b^3}$

Report an Error

Example Question #1 : Simplifying Polynomials

Simplify the following polynomial:

$\frac{-18a^{-2}b^3c^{-4}}{12ab^{-2}c^{-3}}$

Possible Answers:

$\frac{-3b^5}{2a^3c^2}$

$\frac{-3b^4}{2a^3c}$

$\frac{-3b^5}{2a^3c}$

$\frac{-3b^5}{2ac}$

$\frac{-5b^5}{2a^3c}$

Correct answer:

$\frac{-3b^5}{2a^3c}$

Explanation:

To simplify the polynomial, begin by rearranging the terms to have positive exponents:

$\frac{-18a^{-2}b^3c^{-4}}{12ab^{-2}c^{-3}}$

$\frac{-18b^3b^2c^{3}}{12aa^2c^{4}}$

Now, combine like terms:

$\frac{-18b^5}{12a^3c^{1}}$

Simplify the integers:

$\frac{-3b^5}{2a^3c}$

Report an Error

Example Question #1 : Simplifying Polynomials

Simplify the following polynomial:

$(5n^{3x}-2m^{x+2})^2$

Possible Answers:

$5n^{6x}-20n^{3x}m^{x+2}+4m^{2x+4}$

$25n^{6x}-20n^{3x}m^{x+2}+4m^{2x+4}$

$10n^{6x}-20n^{3x}m^{x+2}+2m^{2x+4}$

$25n^{6x}-20n^{3x}m^{x+2}+2m^{2x+4}$

$25n^{6x}-10n^{3x}m^{x+2}+4m^{2x+4}$

Correct answer:

$25n^{6x}-20n^{3x}m^{x+2}+4m^{2x+4}$

Explanation:

Squaring the polynomial is equivalent to:

$(5n^{3x}-2m^{x+2})^2$

$(5n^{3x}-2m^{x+2})(5n^{3x}-2m^{x+2})$

Use the FOIL method to multiply the terms:

F - First

O - Outer

I - Inner

L - Last

$25n^{6x}-10n^{3x}m^{x+2}-10n^{3x}m^{x+2}+4m^{2x+4}$

Combine like terms:

$25n^{6x}-20n^{3x}m^{x+2}+4m^{2x+4}$

Report an Error

Example Question #1 : Simplifying Polynomials

Simplify the following polynomial:

$(\frac{-a^{-2}b^3c^{-1}}{3a^{-4}b^{-1}c^3})^{-2}$

Possible Answers:

$\frac{9c^8}{a^{4}b^8}$

$\frac{9c^8}{a^{4}b^4}$

$\frac{c^8}{9a^{2}b^8}$

$\frac{c^8}{9a^{4}b^8}$

$\frac{9c^8}{a^{2}b^8}$

Correct answer:

$\frac{9c^8}{a^{4}b^8}$

Explanation:

To simplify the polynomial, begin by rearranging the terms to have positive exponents:

$(\frac{-a^{-2}b^3c^{-1}}{3a^{-4}b^{-1}c^3})^{-2}$

$(\frac{-a^{4}b^3b^1}{3a^{2}c^3c^1})^{-2}$

Rearrange the terms once again so that the outer exponent is positive. Also, combine like terms:

$(\frac{-3c^4}{a^{2}b^4})^{2}$

Now, square the polynomial:

$\frac{9c^8}{a^{4}b^8}$

Report an Error

Example Question #1 : Polynomials

Simplify the following polynomial:

(5a)(6a^2b)(3ab^3)+(2a)^2(3b^3)(2a^2b)

Possible Answers:

114a^4b^2

114a^2b^4

114a^3b^4

114a^4b^4

114a^4b^3

Correct answer:

114a^4b^4

Explanation:

To simplify the polynomial, begin by combining the terms within the parentheses and multiplying the integers:

(5a)(6a^2b)(3ab^3)+(2a)^2(3b^3)(2a^2b)

90a^4b^4+24a^4b^4

Now, add together like terms:

90a^4b^4+24a^4b^4=114a^4b^4

Report an Error

View Tutors

Cameo
Certified Tutor

University of Oklahoma Norman Campus, Bachelor of Science, Environmental Engineering.

View Tutors

Jonathan
Certified Tutor

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

View Tutors

Yongmao
Certified Tutor

Nankai University, Bachelor of Science, Chemistry. Washington University in St Louis, Doctor of Philosophy, Organic Chemistry.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in Chicago, LSAT Tutors in Los Angeles, Reading Tutors in New York City, Reading Tutors in Washington DC, Statistics Tutors in Washington DC, Biology Tutors in San Francisco-Bay Area, Calculus Tutors in Houston, Statistics Tutors in Phoenix, English Tutors in New York City, Computer Science Tutors in Atlanta

Popular Courses & Classes

ACT Courses & Classes in Miami, Spanish Courses & Classes in Houston, GMAT Courses & Classes in Miami, LSAT Courses & Classes in San Diego, Spanish Courses & Classes in Boston, SSAT Courses & Classes in Atlanta, MCAT Courses & Classes in Denver, GRE Courses & Classes in Boston, LSAT Courses & Classes in Phoenix, ISEE Courses & Classes in Dallas Fort Worth

Popular Test Prep

GMAT Test Prep in Atlanta, LSAT Test Prep in Atlanta, LSAT Test Prep in New York City, SAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Dallas Fort Worth, MCAT Test Prep in Philadelphia, ISEE Test Prep in Atlanta, SSAT Test Prep in Los Angeles, LSAT Test Prep in Phoenix, MCAT Test Prep in Washington DC

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

High School Math : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Polynomials

Example Question #1 : Simplifying Polynomials

Example Question #1 : Polynomials

Example Question #2 : Simplifying Polynomials

Example Question #3 : Simplifying Polynomials

Example Question #1 : Simplifying Polynomials

Example Question #1 : Simplifying Polynomials

Example Question #1 : Simplifying Polynomials

Example Question #1 : Simplifying Polynomials

Example Question #1 : Polynomials

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: