Call Now to Set Up Tutoring:

(888) 888-0446

Pre-Algebra : Polynomials

Study concepts, example questions & explanations for Pre-Algebra

Create An Account

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Multiplying And Dividing Polynomials

Multiply: (x^2+2)(-x^3+3x-1)

Possible Answers:

-x^6+x^3-x^2+6x-2

-x^6+3x^3-x^2+6x-2

-x^5+x^3-x^2+6x-2

-x^5+3x^3-x^2+6x-2

Correct answer:

-x^5+x^3-x^2+6x-2

Explanation:

(x^2+2)(-x^3+3x-1)=-x^5+3x^3-x^2-2x^3+6x-2

=-x^5+x^3-x^2+6x-2

Report an Error

Example Question #3 : Multiplying And Dividing Polynomials

Simplify:

$\left ( 3x^{2}+4 \right )\left ( x^{3}+2x^{2}-5 \right )$

Possible Answers:

$3x^{5}+6x^{4}+4x^{3}+7x^{2}+20$

$3x^{5}+6x^{4}+x^{3}-13x^{2}-5$

$3x^{5}+6x^{4}+4x^{3}-7x^{2}-20$

$4x^{3}+11x^{2}-16$

$7x^{6}+6x^{4}+8x^{2}-20$

Correct answer:

$3x^{5}+6x^{4}+4x^{3}-7x^{2}-20$

Explanation:

When multiplying, remember the Product Rule of Exponents: $x^{m}*x^{n}=x^{m+n}$

Step 1: Multiply the first term of the first polynomial across the terms of the second polynomial, and then add those products:

$\left ( 3x^{2}*x^{3} \right )+\left ( 3x^{2}*2x^{2} \right )+\left (3x^{2}*-5 \right )$
$3x^{5}+6x^{4}-15x^{2}$ Step 2: Multiply the second term of the first polynomial across the terms of the second polynomial, and again add the products:

$\left ( 4*x^{3} \right )+\left ( 4*2x^{2} \right )+\left (4*-5 \right )$

$4x^{3}+8x^{2}-20$

Step 3: Add the products from Step 1 and Step 2 by combining like terms. Remember that variables with different exponents are not like terms. For example, $-15x^{2}$ and $8x^{2}$ are like terms, but, $8x^{2}$ and $4x^{3}$ are not like terms: $3x^{5}+6x^{4}-15x^{2}+4x^{3}+8x^{2}-20$

$3x^{5}+6x^{4}+4x^{3}-15x^{2}+8x^{2}-20$

$3x^{5}+6x^{4}+4x^{3}-7x^{2}-20$

Report an Error

Example Question #4 : Multiplying And Dividing Polynomials

Expand the following:

$\small (x+7)(x-2)$

Possible Answers:

$\small x^2+9x+9$

$\small x^2-5x-14$

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

$\small x^2+9x+14$

$\small x^2+5x-14$

Correct answer:

$\small x^2+5x-14$

Explanation:

Recall that when expanding polynomials, we use the term FOIL (First, Outside, Inside, Last) to help us multiply all terms together.

$\small (x+7)(x-2)$

$\small \small (x)(x)+(x)(-2)+(7)(x)+(7)(-2)$

Next, multiply each term to simplify and combine like terms. Note: Be careful with negative signs.

$\small x^2-2x+7x-14$

$\small x^2+5x-14$

Report an Error

Example Question #1 : Multiplying And Dividing Polynomials

Simplify:

$4m\cdot3m$

Possible Answers:

$6m^{2}$

24m

12m

$12m^{3}$

$12m^{2}$

Correct answer:

$12m^{2}$

Explanation:

To solve, you can use the commutative and associative properties of multiplication to group like-terms together.

$4m\cdot3m=4\times m\times 3\times m=4\times3\times m\times m$

The 4 and 3 should be first multiplied, resulting in 12.

$12\times m\times m$

Next should be multiplied by , giving us $m^{2}$ .

$12\times m^2$

12 times $m^{2}$ is equal to $12m^{2}$ .

Therefore, the correct answer is $12m^{2}$ .

Report an Error

Example Question #1 : Multiplying And Dividing Polynomials

Multiply:

4x(3x-2)

Possible Answers:

12x^2-8x

12x-8

12x^2+8x

12x+8

Correct answer:

12x^2-8x

Explanation:

Use the distributive property:

$4x(3x-2)=(4x\times3x)-(4x\times2)=12x^2-8x$

Report an Error

Example Question #1 : Multiplying And Dividing Polynomials

Multiply:

$\left (100Y^{2}- 70Y + 49 \right )(10Y+7)$

Possible Answers:

$1,000Y^{3} + 343$

$1,000Y^{3} + 700Y^{2}- 490 Y- 343$

$1,000Y^{3}+ 100Y^{2}-49 Y- 343$

$1,000Y^{3} - 700Y^{2}+ 490 Y- 343$

$1,000Y^{3} - 100Y^{2}+49 Y- 343$

Correct answer:

$1,000Y^{3} + 343$

Explanation:

$\left (100Y^{2}- 70Y + 49 \right )(10Y+7)$

$= \left [\left (10Y \right )^{2}- 10Y\cdot 7 +7^{2} \right ](10Y+7)$

This product fits the sum of cubes pattern, where A = 10Y, B = 7 :

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

$\left [\left (10Y \right )^{2}- 10Y\cdot 7 +7^{2} \right ](10Y+7)$

$= (10Y)^{3}+7^{3} = 1,000Y^{3} + 343$

Report an Error

Example Question #1 : How To Divide Polynomials

Simplify: $\frac{6x^7y^3z^9}{3x^6y^3z}$

Possible Answers:

xyz^8

2xz^8

6xyz^8

xz^8

xyz

Correct answer:

2xz^8

Explanation:

Cancel by subtracting the exponents of like terms:

$\frac{6x^7y^3z^9}{3x^6y^3z} = 2x^{7-6}y^{3-3}z^{9-1}=2xy^0z^8=2xz^8$

Report an Error

Example Question #4 : Multiplying And Dividing Polynomials

Simplify the following expression:

(x+4)(x-5)

Possible Answers:

$=x^{2}+9x+20$

$=x^{2}-x-20$

=-x

=2x-1

= $x^{2}-20$

Correct answer:

$=x^{2}-x-20$

Explanation:

Use FOIL (First Outer Inner Last).

(x+4)(x-5)

=x(x-5)+4(x-5)

$=x^{2}-5x+4x-20$

$=x^{2}-x-20$

Report an Error

Example Question #5 : Multiplying And Dividing Polynomials

Expand the following expression:

$(x+1)^{3}$

Possible Answers:

$=x^{3}+3x^{2}+3x+1$

$=3x^{3}+3x^{2}+3x+3$

$=x^{3}+1$

$=x^{3}+x+1$

$=x^{3}+x^{2}+x+1$

Correct answer:

$=x^{3}+3x^{2}+3x+1$

Explanation:

Use FOIL to expand the polynomial.

$(x+1)^{3}$

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

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

$=x^{3}+2x^{2}+x+x^{2}+2x+1$

$=x^{3}+3x^{2}+3x+1$

Report an Error

Example Question #41 : Polynomials

Simplify this expression:

$\frac{x^3+6x^2+5x}{x^2(x^2+3x+2)}$

Possible Answers:

$\frac{x+2}{x(x+5)}$

$\frac{x+5}{(x+2)}$

$\frac{x+2}{(x+5)}$

$\frac{x+5}{x}$

$\frac{x+5}{x(x+2)}$

Correct answer:

$\frac{x+5}{x(x+2)}$

Explanation:

First factor each equation fully to see if there are terms that can cancel out:

$\frac{x^3+6x^2+5x}{x^2(x^2+3x+2)}$

$\frac{x(x^2+6x+5)}{x^2(x^2+3x+2)}$

$\frac{x(x+5)(x+1)}{x^2(x+1)(x+2)}$

Cancel terms:

$\frac{x(x+5){\color{Red} (x+1)}}{x^2{\color{Red} (x+1)}(x+2)}$

$\frac{x(x+5)}{x^2(x+2)}$

Simplify exponents:

$\frac{(x+5)}{x(x+2)}$

Report an Error

View Pre-Algebra Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

View Pre-Algebra Tutors

Joseph
Certified Tutor

Old Dominion University, Bachelor of Science, Electrical Engineering. Western Governors University, Masters in Education, Mat...

View Pre-Algebra Tutors

Nicole
Certified Tutor

Liberty University, Bachelor of Science, Psychology. Liberty University, Master of Arts, Mental Health Counseling.

All Pre-Algebra Resources

11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Washington DC, Algebra Tutors in Philadelphia, MCAT Tutors in New York City, MCAT Tutors in Washington DC, Physics Tutors in Miami, ISEE Tutors in Denver, GMAT Tutors in San Francisco-Bay Area, GMAT Tutors in San Diego, SAT Tutors in Philadelphia, French Tutors in San Diego

Popular Courses & Classes

MCAT Courses & Classes in New York City, ISEE Courses & Classes in Philadelphia, ISEE Courses & Classes in Seattle, LSAT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Miami, MCAT Courses & Classes in Seattle, GMAT Courses & Classes in San Diego, Spanish Courses & Classes in Los Angeles, SSAT Courses & Classes in Washington DC, ISEE Courses & Classes in Washington DC

Popular Test Prep

ISEE Test Prep in Seattle, ISEE Test Prep in Washington DC, SAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Miami, ISEE Test Prep in Atlanta, MCAT Test Prep in Atlanta, GRE Test Prep in San Francisco-Bay Area, MCAT Test Prep in Seattle, ACT Test Prep in Los Angeles, ISEE Test Prep in Los Angeles

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

Pre-Algebra : Polynomials

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #2 : Multiplying And Dividing Polynomials

Example Question #3 : Multiplying And Dividing Polynomials

Example Question #4 : Multiplying And Dividing Polynomials

Example Question #1 : Multiplying And Dividing Polynomials

Example Question #1 : Multiplying And Dividing Polynomials

Example Question #1 : Multiplying And Dividing Polynomials

Example Question #1 : How To Divide Polynomials

Example Question #4 : Multiplying And Dividing Polynomials

Example Question #5 : Multiplying And Dividing Polynomials

Example Question #41 : Polynomials

All Pre-Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: