Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: High School - Algebra : High School: Algebra

Study concepts, example questions & explanations for Common Core: High School - Algebra

Create An Account

All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #17 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when $13 x^{2} + 9 x - 6$ is divided by x - 10

Possible Answers:

1390

122

100

Correct answer:

1390

Explanation:

In order to solve this problem, we need to perform synthetic division. We set up synthetic division by writing down the zero of the expression we are dividing by, and the coefficients of the polynomial on a line.

$\begin{tabular}{ c| ccc}10&13&9&-6\\ ~ & ~ & ~ & ~ \\ \hline ~ & ~ & ~ & ~ \end{tabular}$

The first step is to bring the coefficient of the $\uptext{x}^2$ term down.

$\begin{tabular}{ c| ccc}10&13&9&-6\\ ~ & ~ & ~ & ~ \\ \hline ~ &13& ~ & ~ \end{tabular}$

Now we multiply the zero by the term we just put down, and place it under the $\uptext{x}$ term coefficient.

$\begin{tabular}{ c| ccc}10&13&9&-6\\ ~ & ~ &130& ~ \\ \hline ~ &13& ~ & ~ \end{tabular}$

Now we add the column up to get.

$\begin{tabular}{ c| ccc}10&13&9&-6\\~ & ~ &130& ~ \\ \hline ~ &13&139& ~ \end{tabular}$

Now we multiply the number we got by the zero, and place it under the constant term.

$\begin{tabular}{ c| ccc}10&13&9&-6\\ ~ & ~ &130&1390\\ \hline ~ &13&139& ~ \end{tabular}$

Now we add the column together to get.

$\begin{tabular}{ c| ccc}10&13&9&-6\\ ~ & ~ &130&1390\\ \hline ~ &13&139&1384\end{tabular}$

The last number is the remainder, so our final answer is 1384 .

Report an Error

Example Question #18 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when $- 11 x^{2} + 19 x + 4$ is divided by x + 6

Possible Answers:

Correct answer:

Explanation:

$\begin{tabular}{ c| ccc}-6&-11&19&4\\ ~ & ~ & ~ & ~ \\ \hline ~ & ~ & ~ & ~ \end{tabular}$

The first step is to bring the coefficient of the $\uptext{x}^2$ term down.

$\begin{tabular}{ c| ccc}-6&-11&19&4\\ ~ & ~ & ~ & ~ \\ \hline ~ &-11& ~ & ~ \end{tabular}$

Now we multiply the zero by the term we just put down, and place it under the $\uptext{x}$ term coefficient.

$\begin{tabular}{ c| ccc}-6&-11&19&4\\ ~ & ~ &66& ~ \\ \hline ~ &-11& ~ & ~ \end{tabular}$

Now we add the column up to get.

$\begin{tabular}{ c| ccc}-6&-11&19&4\\~ & ~ &66& ~ \\ \hline ~ &-11&85& ~ \end{tabular}$

Now we multiply the number we got by the zero, and place it under the constant term.

$\begin{tabular}{ c| ccc}-6&-11&19&4\\ ~ & ~ &66&-510\\ \hline ~ &-11&85& ~ \end{tabular}$

Now we add the column together to get.

$\begin{tabular}{ c| ccc}-6&-11&19&4\\ ~ & ~ &66&-510\\ \hline ~ &-11&85&-506\end{tabular}$

The last number is the remainder, so our final answer is .

Report an Error

Example Question #31 : Arithmetic With Polynomials & Rational Expressions

What is the remainder when $- 11 x^{2} + 19 x + 4$ is divided by x - 13

Possible Answers:

169

177

Correct answer:

Explanation:

$\begin{tabular}{ c| ccc}13&-11&19&4\\ ~ & ~ & ~ & ~ \\ \hline ~ & ~ & ~ & ~ \end{tabular}$

The first step is to bring the coefficient of the $\uptext{x}^2$ term down.

$\begin{tabular}{ c| ccc}13&-11&19&4\\ ~ & ~ & ~ & ~ \\ \hline ~ &-11& ~ & ~ \end{tabular}$

Now we multiply the zero by the term we just put down, and place it under the $\uptext{x}$ term coefficient.

$\begin{tabular}{ c| ccc}13&-11&19&4\\ ~ & ~ &-143& ~ \\ \hline ~ &-11& ~ & ~ \end{tabular}$

Now we add the column up to get.

$\begin{tabular}{ c| ccc}13&-11&19&4\\~ & ~ &-143& ~ \\ \hline ~ &-11&-124& ~ \end{tabular}$

Now we multiply the number we got by the zero, and place it under the constant term.

$\begin{tabular}{ c| ccc}13&-11&19&4\\ ~ & ~ &-143&-1612\\ \hline ~ &-11&-124& ~ \end{tabular}$

Now we add the column together to get.

$\begin{tabular}{ c| ccc}13&-11&19&4\\ ~ & ~ &-143&-1612\\ \hline ~ &-11&-124&-1608\end{tabular}$

The last number is the remainder, so our final answer is .

Report an Error

Example Question #101 : High School: Algebra

What is the remainder when $2 x^{2} - 19 x + 8$ is divided by x - 18

Possible Answers:

307

324

306

Correct answer:

306

Explanation:

$\begin{tabular}{ c| ccc}18&2&-19&8\\ ~ & ~ & ~ & ~ \\ \hline ~ & ~ & ~ & ~ \end{tabular}$

The first step is to bring the coefficient of the $\uptext{x}^2$ term down.

$\begin{tabular}{ c| ccc}18&2&-19&8\\ ~ & ~ & ~ & ~ \\ \hline ~ &2& ~ & ~ \end{tabular}$

Now we multiply the zero by the term we just put down, and place it under the $\uptext{x}$ term coefficient.

$\begin{tabular}{ c| ccc}18&2&-19&8\\ ~ & ~ &36& ~ \\ \hline ~ &2& ~ & ~ \end{tabular}$

Now we add the column up to get.

$\begin{tabular}{ c| ccc}18&2&-19&8\\~ & ~ &36& ~ \\ \hline ~ &2&17& ~ \end{tabular}$

Now we multiply the number we got by the zero, and place it under the constant term.

$\begin{tabular}{ c| ccc}18&2&-19&8\\ ~ & ~ &36&306\\ \hline ~ &2&17& ~ \end{tabular}$

Now we add the column together to get.

$\begin{tabular}{ c| ccc}18&2&-19&8\\ ~ & ~ &36&306\\ \hline ~ &2&17&314\end{tabular}$

The last number is the remainder, so our final answer is 314 .

Report an Error

Example Question #21 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when $- 20 x^{2} - 5 x - 9$ is divided by x + 8

Possible Answers:

Correct answer:

Explanation:

$\begin{tabular}{ c| ccc}-8&-20&-5&-9\\ ~ & ~ & ~ & ~ \\ \hline ~ & ~ & ~ & ~ \end{tabular}$

The first step is to bring the coefficient of the $\uptext{x}^2$ term down.

$\begin{tabular}{ c| ccc}-8&-20&-5&-9\\ ~ & ~ & ~ & ~ \\ \hline ~ &-20& ~ & ~ \end{tabular}$

Now we multiply the zero by the term we just put down, and place it under the $\uptext{x}$ term coefficient.

$\begin{tabular}{ c| ccc}-8&-20&-5&-9\\ ~ & ~ &160& ~ \\ \hline ~ &-20& ~ & ~ \end{tabular}$

Now we add the column up to get.

$\begin{tabular}{ c| ccc}-8&-20&-5&-9\\~ & ~ &160& ~ \\ \hline ~ &-20&155& ~ \end{tabular}$

Now we multiply the number we got by the zero, and place it under the constant term.

$\begin{tabular}{ c| ccc}-8&-20&-5&-9\\ ~ & ~ &160&-1240\\ \hline ~ &-20&155& ~ \end{tabular}$

Now we add the column together to get.

$\begin{tabular}{ c| ccc}-8&-20&-5&-9\\ ~ & ~ &160&-1240\\ \hline ~ &-20&155&-1249\end{tabular}$

The last number is the remainder, so our final answer is .

Report an Error

Example Question #22 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when $- 2 x^{2} + 19 x + 4$ is divided by x - 8

Possible Answers:

Correct answer:

Explanation:

$\begin{tabular}{ c| ccc}8&-2&19&4\\ ~ & ~ & ~ & ~ \\ \hline ~ & ~ & ~ & ~ \end{tabular}$

The first step is to bring the coefficient of the $\uptext{x}^2$ term down.

$\begin{tabular}{ c| ccc}8&-2&19&4\\ ~ & ~ & ~ & ~ \\ \hline ~ &-2& ~ & ~ \end{tabular}$

Now we multiply the zero by the term we just put down, and place it under the $\uptext{x}$ term coefficient.

$\begin{tabular}{ c| ccc}8&-2&19&4\\ ~ & ~ &-16& ~ \\ \hline ~ &-2& ~ & ~ \end{tabular}$

Now we add the column up to get.

$\begin{tabular}{ c| ccc}8&-2&19&4\\~ & ~ &-16& ~ \\ \hline ~ &-2&3& ~ \end{tabular}$

Now we multiply the number we got by the zero, and place it under the constant term.

$\begin{tabular}{ c| ccc}8&-2&19&4\\ ~ & ~ &-16&24\\ \hline ~ &-2&3& ~ \end{tabular}$

Now we add the column together to get.

$\begin{tabular}{ c| ccc}8&-2&19&4\\ ~ & ~ &-16&24\\ \hline ~ &-2&3&28\end{tabular}$

The last number is the remainder, so our final answer is .

Report an Error

Example Question #23 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when $- 15 x^{2} + 9 x - 3$ is divided by x - 3

Possible Answers:

Correct answer:

Explanation:

$\begin{tabular}{ c| ccc}3&-15&9&-3\\ ~ & ~ & ~ & ~ \\ \hline ~ & ~ & ~ & ~ \end{tabular}$

The first step is to bring the coefficient of the $\uptext{x}^2$ term down.

$\begin{tabular}{ c| ccc}3&-15&9&-3\\ ~ & ~ & ~ & ~ \\ \hline ~ &-15& ~ & ~ \end{tabular}$

Now we multiply the zero by the term we just put down, and place it under the $\uptext{x}$ term coefficient.

$\begin{tabular}{ c| ccc}3&-15&9&-3\\ ~ & ~ &-45& ~ \\ \hline ~ &-15& ~ & ~ \end{tabular}$

Now we add the column up to get.

$\begin{tabular}{ c| ccc}3&-15&9&-3\\~ & ~ &-45& ~ \\ \hline ~ &-15&-36& ~ \end{tabular}$

Now we multiply the number we got by the zero, and place it under the constant term.

$\begin{tabular}{ c| ccc}3&-15&9&-3\\ ~ & ~ &-45&-108\\ \hline ~ &-15&-36& ~ \end{tabular}$

Now we add the column together to get.

$\begin{tabular}{ c| ccc}3&-15&9&-3\\ ~ & ~ &-45&-108\\ \hline ~ &-15&-36&-111\end{tabular}$

The last number is the remainder, so our final answer is .

Report an Error

Example Question #24 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when $4 x^{2} - 17 x - 2$ is divided by x - 2

Possible Answers:

Correct answer:

Explanation:

$\begin{tabular}{ c| ccc}2&4&-17&-2\\ ~ & ~ & ~ & ~ \\ \hline ~ & ~ & ~ & ~ \end{tabular}$

The first step is to bring the coefficient of the $\uptext{x}^2$ term down.

$\begin{tabular}{ c| ccc}2&4&-17&-2\\ ~ & ~ & ~ & ~ \\ \hline ~ &4& ~ & ~ \end{tabular}$

Now we multiply the zero by the term we just put down, and place it under the $\uptext{x}$ term coefficient.

$\begin{tabular}{ c| ccc}2&4&-17&-2\\ ~ & ~ &8& ~ \\ \hline ~ &4& ~ & ~ \end{tabular}$

Now we add the column up to get.

$\begin{tabular}{ c| ccc}2&4&-17&-2\\~ & ~ &8& ~ \\ \hline ~ &4&-9& ~ \end{tabular}$

Now we multiply the number we got by the zero, and place it under the constant term.

$\begin{tabular}{ c| ccc}2&4&-17&-2\\ ~ & ~ &8&-18\\ \hline ~ &4&-9& ~ \end{tabular}$

Now we add the column together to get.

$\begin{tabular}{ c| ccc}2&4&-17&-2\\ ~ & ~ &8&-18\\ \hline ~ &4&-9&-20\end{tabular}$

The last number is the remainder, so our final answer is .

Report an Error

Example Question #25 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when $7 x^{2} - 3 x + 1$ is divided by x - 16

Possible Answers:

256

260

1744

Correct answer:

1744

Explanation:

$\begin{tabular}{ c| ccc}16&7&-3&1\\ ~ & ~ & ~ & ~ \\ \hline ~ & ~ & ~ & ~ \end{tabular}$

The first step is to bring the coefficient of the $\uptext{x}^2$ term down.

$\begin{tabular}{ c| ccc}16&7&-3&1\\ ~ & ~ & ~ & ~ \\ \hline ~ &7& ~ & ~ \end{tabular}$

Now we multiply the zero by the term we just put down, and place it under the $\uptext{x}$ term coefficient.

$\begin{tabular}{ c| ccc}16&7&-3&1\\ ~ & ~ &112& ~ \\ \hline ~ &7& ~ & ~ \end{tabular}$

Now we add the column up to get.

$\begin{tabular}{ c| ccc}16&7&-3&1\\~ & ~ &112& ~ \\ \hline ~ &7&109& ~ \end{tabular}$

Now we multiply the number we got by the zero, and place it under the constant term.

$\begin{tabular}{ c| ccc}16&7&-3&1\\ ~ & ~ &112&1744\\ \hline ~ &7&109& ~ \end{tabular}$

Now we add the column together to get.

$\begin{tabular}{ c| ccc}16&7&-3&1\\ ~ & ~ &112&1744\\ \hline ~ &7&109&1745\end{tabular}$

The last number is the remainder, so our final answer is 1745 .

Report an Error

Example Question #26 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

What is the remainder when $- 8 x^{2} + 6 x - 8$ is divided by x - 8

Possible Answers:

Correct answer:

Explanation:

$\begin{tabular}{ c| ccc}8&-8&6&-8\\ ~ & ~ & ~ & ~ \\ \hline ~ & ~ & ~ & ~ \end{tabular}$

The first step is to bring the coefficient of the $\uptext{x}^2$ term down.

$\begin{tabular}{ c| ccc}8&-8&6&-8\\ ~ & ~ & ~ & ~ \\ \hline ~ &-8& ~ & ~ \end{tabular}$

Now we multiply the zero by the term we just put down, and place it under the $\uptext{x}$ term coefficient.

$\begin{tabular}{ c| ccc}8&-8&6&-8\\ ~ & ~ &-64& ~ \\ \hline ~ &-8& ~ & ~ \end{tabular}$

Now we add the column up to get.

$\begin{tabular}{ c| ccc}8&-8&6&-8\\~ & ~ &-64& ~ \\ \hline ~ &-8&-58& ~ \end{tabular}$

Now we multiply the number we got by the zero, and place it under the constant term.

$\begin{tabular}{ c| ccc}8&-8&6&-8\\ ~ & ~ &-64&-464\\ \hline ~ &-8&-58& ~ \end{tabular}$

Now we add the column together to get.

$\begin{tabular}{ c| ccc}8&-8&6&-8\\ ~ & ~ &-64&-464\\ \hline ~ &-8&-58&-472\end{tabular}$

The last number is the remainder, so our final answer is .

Report an Error

View Tutors

Tharun
Certified Tutor

New York University, Bachelor of Science, Finance.

View Tutors

Thomas
Certified Tutor

Texas State University-San Marcos, Bachelor of Science, Computer Science.

View Tutors

Robert
Certified Tutor

Rensselaer Polytechnic Institute, Bachelors, Electrical Engineering. Brooklyn Polytechnic, Masters, Computer Science.

All Common Core: High School - Algebra Resources

8 Diagnostic Tests 97 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in San Diego, Reading Tutors in Miami, Spanish Tutors in Denver, Math Tutors in San Diego, Biology Tutors in New York City, Physics Tutors in Philadelphia, GMAT Tutors in Boston, Math Tutors in Atlanta, Reading Tutors in Los Angeles, Computer Science Tutors in New York City

Popular Courses & Classes

GRE Courses & Classes in Chicago, SAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Philadelphia, GMAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Washington DC, MCAT Courses & Classes in New York City, GRE Courses & Classes in Houston, MCAT Courses & Classes in Chicago, ISEE Courses & Classes in Dallas Fort Worth

Popular Test Prep

GRE Test Prep in San Francisco-Bay Area, MCAT Test Prep in San Diego, SSAT Test Prep in Dallas Fort Worth, GMAT Test Prep in Boston, ISEE Test Prep in Dallas Fort Worth, ACT Test Prep in Los Angeles, SSAT Test Prep in Phoenix, SAT Test Prep in Phoenix, LSAT Test Prep in Miami, GRE Test Prep in Chicago

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

Common Core: High School - Algebra : High School: Algebra

Study concepts, example questions & explanations for Common Core: High School - Algebra

All Common Core: High School - Algebra Resources

Example Questions

Example Question #17 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

Example Question #18 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

Example Question #31 : Arithmetic With Polynomials & Rational Expressions

Example Question #101 : High School: Algebra

Example Question #21 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

Example Question #22 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

Example Question #23 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

Example Question #24 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

Example Question #25 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

Example Question #26 : Remainder Theorem: Ccss.Math.Content.Hsa Apr.B.2

All Common Core: High School - Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: