Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Binomials

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : How To Find The Value Of The Coefficient

Give the coefficient of $x^{2}$ in the product

$\left ( 2x + \frac{1}{3}\right ) \left ( x- \frac{1}{6}\right ) \left ( x+ \frac{1}{4}\right )$

Possible Answers:

$\frac{11}{12}$

$\frac{1}{4}$

$\frac{7}{6}$

$\frac{1}{2}$

$\frac{1}{6}$

Correct answer:

$\frac{1}{2}$

Explanation:

While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that two terms and one constant are multiplied; find the three products and add them, as follows:

$\left ( \underline{2x }+ \frac{1}{3}\right ) \left ( \underline{x}- \frac{1}{6}\right ) \left ( x\underline{+ \frac{1}{4}}\right )$

$2x \cdot x \cdot \frac{1}{4} = \frac{1}{2}x^{2}$

$\left ( \underline{2x }+ \frac{1}{3}\right ) \left ( x \underline{- \frac{1}{6}}\right ) \left ( \underline{x}+ \frac{1}{4}\right )$

$2x \cdot \left (- \frac{1}{6} \right ) \cdot x = - \frac{1}{3}x^{2}$

$\left ( 2x\underline{ + \frac{1}{3}}\right ) \left ( \underline{x}- \frac{1}{6}\right ) \left ( \underline{x}+ \frac{1}{4}\right )$

$\frac{1}{3} \cdot x \cdot x= \frac{1}{3}x^{2}$

Add: $\frac{1}{2}x^{2} +\left ( - \frac{1}{3}x^{2} \right ) + \frac{1}{3}x^{2} = \frac{1}{2}x^{2}$

The correct response is $\frac{1}{2}$ .

Report an Error

Example Question #3 : How To Find The Value Of The Coefficient

Give the coefficient of $x^{5}$ in the binomial expansion of $\left ( 2x+ 0.5\right )^{8}$ .

Possible Answers:

1,680

224

26,880

Correct answer:

224

Explanation:

If the expression $\left ( A x + B\right )^{n}$ is expanded, then by the binomial theorem, the $x^{k}$ term is

$C(n, k) \cdot\left ( Ax \right )^{k} \cdot B ^{n - k}$

$= C(n, k) \cdot A ^{k} \cdot B ^{n - k} \cdot x^{k}$

or, equivalently, the coefficient of $x^{k}$ is

$C(n, k) \cdot A ^{k} \cdot B ^{n - k}$

Therefore, the $x^{5}$ coefficient can be determined by setting

A = 2, B =0.5, k=5, n = 8 :

$C(8,5) \cdot 2^{5} \cdot 0.5 ^{8-5}$

$=C(8,5) \cdot 2^{5} \cdot 0.5 ^{3}$

$= 56\cdot 32 \cdot 0.125$

=224

Report an Error

Example Question #1 : How To Find The Value Of The Coefficient

Give the coefficient of $x^{4}$ in the binomial expansion of $\left (6x+ \frac{1}{6}\right )^{7}$ .

Possible Answers:

$\frac{35}{6}$

140

210

5,040

Correct answer:

210

Explanation:

If the expression $\left ( A x + B\right )^{n}$ is expanded, then by the binomial theorem, the $x^{k}$ term is

$C(n, k) \cdot\left ( Ax \right )^{k} \cdot B ^{n - k}$

$= C(n, k) \cdot A ^{k} \cdot B ^{n - k} \cdot x^{k}$

or, equivalently, the coefficient of $x^{k}$ is

$C(n, k) \cdot A ^{k} \cdot B ^{n - k}$

Therefore, the $x^{4}$ coefficient can be determined by setting

$A = 6, B = \frac{1}{6}, n = 7, k= 4$ :

$C(7,4) \cdot 6 ^{4} \cdot\left ( \frac{1}{6} \right ) ^{7-4}$

$=C(7,4) \cdot 6 ^{4} \cdot\left ( \frac{1}{6} \right ) ^{3}$

$=35 \cdot 1,296 \cdot \frac{1}{216}$

= 210

Report an Error

Example Question #3 : How To Find The Value Of The Coefficient

Give the coefficient of $x^{5}$ in the binomial expansion of $\left ( 0.2x+ 5 \right )^{7}$ .

Possible Answers:

20.16

2,625

315,000

0.168

Correct answer:

0.168

Explanation:

If the expression $\left ( A x + B\right )^{n}$ is expanded, then by the binomial theorem, the $x^{k}$ term is

$C(n, k) \cdot\left ( Ax \right )^{k} \cdot B ^{n - k}$

$= C(n, k) \cdot A ^{k} \cdot B ^{n - k} \cdot x^{k}$

or, equivalently, the coefficient of $x^{k}$ is

$C(n, k) \cdot A ^{k} \cdot B ^{n - k}$

Therefore, the $x^{5}$ coefficient can be determined by setting

A = 0.2, B =5, k=5, n = 7

$C(7,5) \cdot 0.2^{5} \cdot 5 ^{7 - 5}$

$= C(7,5) \cdot 0.2 ^{5} \cdot 5 ^{2}$

$= 21\cdot 0.00032 \cdot 25$

= 0.168

Report an Error

Example Question #2 : How To Find The Value Of The Coefficient

Give the coefficient of $x^{2}$ in the product

$\left (3x- 7 \right ) \left ( 4x+3\right )\left ( 2x-7\right )$ .

Possible Answers:

158

Correct answer:

Explanation:

$\left (\underline{3x}- 7 \right ) \left ( \underline{4x}+3\right )\left ( 2x\underline{-7}\right )$

$3x \cdot 4x \cdot (-7) = -84x^{2}$

$\left (\underline{3x}- 7 \right ) \left ( 4x\underline{+3}\right )\left ( \underline{2x}-7\right )$

$3x \cdot 3 \cdot 2x = 18x^{2}$

$\left (3x\underline{- 7} \right ) \left ( \underline{4x}+3\right )\left ( \underline{2x}-7\right )$

$-7 \cdot 4x \cdot 2x = -56x^{2}$

Add: $-84x^{2} + 18x^{2} - 56x^{2} = -122x^{2}$

The correct response is -122.

Report an Error

Example Question #1 : How To Find The Value Of The Coefficient

What is the value of the coefficient of ? $\frac{3x^2-9x}{x}-4x$

Possible Answers:

Correct answer:

Explanation:

In order to determine the coefficient, we will need to fully simplify this expression.

The numerator of the first term shares an variable, which can be divided.

$\frac{3x^2-9x}{x} = \frac{x(3x-9)}{x} = 3x-9$

Subtract this expression with .

3x-9-4x = -x-9

The coefficient is the number in front of . The coefficient is .

Report an Error

Example Question #1 : How To Find The Solution To A Binomial Problem

Solve for : (x+5)+(3x+15)=0

Possible Answers:

$\frac{20}{3}$

Correct answer:

Explanation:

First, rearrange the equation so that "like terms" are grouped together, like this: 1x+3x+5+15 .

Second, combine "like" terms with the appropriate mathematical function (i.e., addition, subtraction, etc.), so in this problem, you'll be left with 4x+20 .

Third, set the entire equation equal to and solve for :

4x+20=0

4x=-20

$\frac{4x}{4}=\frac{-20}{4}$

x=-5

Report an Error

Example Question #2 : How To Find The Solution To A Binomial Problem

Solve for : (x-3)+(3x-2)=7 .

Possible Answers:

$\frac{1}{2}$

Correct answer:

Explanation:

First, rearrange the equation so that "like terms" are grouped together, like this: 1x+3x-3-2 .

Second, combine "like" terms with the appropriate mathematical function (i.e., addition, subtraction, etc.), so in this problem, you'll be left with

4x-5=7 .

Third, solve for :

4x-5=7

4x=12

$\frac{4x}{4}=\frac{12}{4}$

x=3

Report an Error

Example Question #2 : Finding Roots

Solve for :

(x+3)^2=16

Possible Answers:

x=1

$x=4\ or\ x=-4$

x=-4

$x=1\ or\ x=-7$

Correct answer:

$x=1\ or\ x=-7$

Explanation:

(x+3)^2=16

$\sqrt{(x+3)^2}=\sqrt{16}\textup{}$

$x+3=\pm4$

$x=1\ or\ -7$

Report an Error

Example Question #1 : How To Find The Solution To A Binomial Problem

4x-8y=32

Solve for in terms of .

Possible Answers:

x=8-2y

y=4-0.5x

x = 8 + 2y

y=0.5x-4

Correct answer:

x = 8 + 2y

Explanation:

First, add 8y to both sides of the equation, cancelling out -8y and isolating x to a value in terms of y:

4x - 8y = 32

+8y +8y

4x = 32 + 8y

Then divide both sides of the equation by 4, providing the x-value in terms of y:

x = 8 + 2y

Report an Error

View Algebra Tutors

Mark
Certified Tutor

Murray State University, Bachelor of Science, Mathematics.

View Algebra Tutors

Tajrin
Certified Tutor

CUNY Brooklyn College, Bachelor of Science, Computer Science.

View Algebra Tutors

Kansiyochukwu
Certified Tutor

University of Calgary, Bachelor of Science, Electromechanical Engineering.

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in Washington DC, LSAT Tutors in Dallas Fort Worth, English Tutors in Denver, Math Tutors in Atlanta, English Tutors in New York City, Spanish Tutors in Denver, Math Tutors in Denver, GRE Tutors in Phoenix, Statistics Tutors in Boston, Math Tutors in San Francisco-Bay Area

Popular Courses & Classes

SAT Courses & Classes in Miami, GMAT Courses & Classes in Miami, MCAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Washington DC, ISEE Courses & Classes in Philadelphia, MCAT Courses & Classes in Phoenix, SSAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Phoenix, LSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

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

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

Algebra 1 : Binomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #2 : How To Find The Value Of The Coefficient

Example Question #3 : How To Find The Value Of The Coefficient

Example Question #1 : How To Find The Value Of The Coefficient

Example Question #3 : How To Find The Value Of The Coefficient

Example Question #2 : How To Find The Value Of The Coefficient

Example Question #1 : How To Find The Value Of The Coefficient

Example Question #1 : How To Find The Solution To A Binomial Problem

Example Question #2 : How To Find The Solution To A Binomial Problem

Example Question #2 : Finding Roots

Example Question #1 : How To Find The Solution To A Binomial Problem

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: