We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Pre-Algebra : Adding and Subtracting Polynomials

Study concepts, example questions & explanations for Pre-Algebra

Create An Account Create Tests & Flashcards

All Pre-Algebra Resources

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

Example Questions

← Previous 1 2 3 4 Next →

Example Question #11 :Adding And Subtracting Polynomials

Simplify the following expression:

8x + 6 - 2x + 2

Possible Answers:

6x + 8

16-2x

8x + 6

6x^2 + 8

Correct answer:

6x + 8

Explanation:

The simplify this expression, combine like terms. Terms are就像if they have the same variables and powers. To combine them, use addition and/or subtraction of the coefficients. The variables and powers do not change when you are combining.

and -2x are like terms (both have the variable). To combine them, you do 8x - 2x = 6x

6 and 2 are also like terms (both have no variable). To combine them, you do 6 + 2 = 8 .

You now have your simplified expression: 6x + 8 which is the final answer.

Report an Error

Example Question #12 :Adding And Subtracting Polynomials

If $\small \small X= 3a^3 +2a^2 +a$ and $\small Y= 9a^4 +3a +1$ , what is $\small X+Y$ ?

Possible Answers:

$\small \small 9a^4 +3a^3+2a^2+3a+1$

$\small 9a^4 +3a^3+2a^2+4a+1$

$\small 9a^4 + 6a^3 + 2a^2 +a +1$

$\small 12a^{3} + 3a^3 +a +1$

$\small 12a^4 + 2a^2 + 4a +1$

Correct answer:

$\small 9a^4 +3a^3+2a^2+4a+1$

Explanation:

The first step is to write out $\small X+Y$ as

$\small X+ Y= (3a^3 +2a^2 +a) + (9a^4 +3a +1)$

The next step is to re-arrange the expression so it is ordered by exponential degree, as:

$\small X+ Y= (9a^4 +3a^3 +2a^2 +a+3a +1)$

The final step is to sum together like terms and simplify the expression, as follows:

$\small \small \small X+ Y= (9a^4 +3a^3 +2a^2 +(a+3a) +1) = (9a^4 +3a^3 +2a^2 +4a +1)$

Report an Error

Example Question #13 :Adding And Subtracting Polynomials

Simplify.

$5x^{3}+6x-3 - \left ( 3x-2x^{2} +1 \right )$

Possible Answers:

$5x^{3}+2x^{2}+9x-4$

$5x^{3}-2x^{2}+3x-2$

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

$7x^{3}-5x^{2}+3x+1$

Correct answer:

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

Explanation:

First distribute the negative:

$5x^{3}+6x-3+ \left ( -3x+2x^{2}-1 \right )$

Group like terms, meaning terms that have the same variable and same exponent:

$5x^{3}+2x^{2}+6x- 3x-3 -1$

Add the like terms:

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

Report an Error

Example Question #14 :Adding And Subtracting Polynomials

Simplify:

$x^{4}+3x^{2}+14x-(x^4-3x^3+2x^2)$

Possible Answers:

2x^4+3x^3+x^2+14x

2x^3+x^2+14x

3x^3+x^2+14x

3x^3+x^2-14x

-2x^4+3x^3+x^2+14x

Correct answer:

3x^3+x^2+14x

Explanation:

To solve you must first distribute the negative to the parentheses

x^4+3x^2+14x-x^4+3x^3-2x^2

Then you should combine like terms and you are left with

3x^3+x^2+14x

Report an Error

Example Question #15 :Adding And Subtracting Polynomials

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

Possible Answers:

2x^2 -2x + 1

2x^4 -3x + 1

2x^3 - x^2

2x^2 + 4x + 1

3x^2 -2x+1

Correct answer:

3x^2 -2x+1

Explanation:

To simplify, we will combine like terms.

(2x^2 + x) + (x^2 -3x + 1) This has two terms with x^2 , and two terms with, so we will group those together:

2x^2 + x^2 + x - 3x + 1 Now we can add together the like terms. Remember that if a term doesn't have a coefficient [number in front of it], there is only one of them:

3x^2 -2x + 1

Report an Error

Example Question #16 :Adding And Subtracting Polynomials

Simplify the following expression:

(4x+7y)-(2x-5y)

Possible Answers:

=11x+3y

=2x+2y

=6x+12y

=2x+12y

=4(x+y)

Correct answer:

=2x+12y

Explanation:

Combine the like terms (x's together and y's together).

Don't forget to distribute the negative sign through the parenthesis.

(4x+7y)-(2x-5y)

=4x+7y-2x+5y

=4x-2x+7y+5y

=2x+2y

Report an Error

Example Question #17 :Adding And Subtracting Polynomials

Subtract these polynomials: (4x^4-2x^3+x+8)-(2x^5-2x^4+3x+1)

Possible Answers:

-2x^5+2x^4-2x^3-2x+7

Answer is not present.

-2x^5+6x^4-2x^3-2x+7

2x^5+6x^4-2x^3-2x-7

-2x^5+6x^4-2x^3+4x+7

Correct answer:

-2x^5+6x^4-2x^3-2x+7

Explanation:

Distribute appropriate sign and simplify:

(4x^4-2x^3+x+8)-(2x^5-2x^4+3x+1)

${\color{Green} 4x^4}-2x^3+x+8-2x^5+{\color{Green} 2x^4}-3x-1$

${\color{Green} 6x^4}-2x^3+{\color{Red} x}+8-2x^5-{\color{Red} 3x}-1$

${\color{Green} 6x^4}-2x^3-{\color{Red} 2x}+{\color{Blue} 8}-2x^5-{\color{Blue} 1}$

${\color{Green} 6x^4}-2x^3+{\color{Red} 2x}+{\color{Blue} 7}-2x^5$

Rearrange into standard form(descending degree or powers):

-2x^5+6x^4-2x^3-2x+7

Report an Error

Example Question #18 :Adding And Subtracting Polynomials

Add the following polynomials:

(3x + 7y - 5z) + (-2x - 6y + 4z) =

Possible Answers:

5x + 13y + 9z

x + y - z

x + y + 9z

x + 13y + z

x + y + z

Correct answer:

x + y - z

Explanation:

(3x + 7y - 5z) + (- 2x - 6y + 4z) =

3x + 7y - 5z + - 2x - 6y + 4z =

(3x - 2x) (7y - 6y) (-5z + 4z) =

x + y - z

Report an Error

Example Question #19 :Adding And Subtracting Polynomials

Simplify the expression.

$3a^{2} + 10a^{2} - 5b^{2}$

Possible Answers:

$8ab^{2}$

$13a^{4}- 5b^{2 }$

$13a^{2} - 5b^{2}$

Correct answer:

$13a^{2} - 5b^{2}$

Explanation:

When adding or subtracting polynomials with exponents, the value of the exponent never changes. The exponent does change when multiplying or dividing.

Start by categorizing each polynomial into groups according to the variable, then according to the like variable's exponent. Because $3a^{2}$ and $10a^{2}$ share a common variable AND exponent, you may add the coefficients:

$3a^{2} + 10 a^{2} = 13a^{2 }$

However, because $5b^{2}$ does not share the same variable, you may not subtract it from $13a^{2 }$ . Therefore, you leave the rest as is:

$13a^{2} - 5b^{2}$

Report an Error

Example Question #20 :Adding And Subtracting Polynomials

Solve: -(x^2+3x)-(x^2-3x)

Possible Answers:

-2x^2+6x

-2x^2

-2x^2-6x

Correct answer:

-2x^2

Explanation:

To simplify this expression, it is necessary to eliminate the parentheses grouping the terms. Distribute the negative signs. Double negative translate the sign to a positive.

-(x^2+3x)-(x^2-3x) = -x^2-3x - x^2+3x

The answer is -2x^2 .

Report an Error

← Previous 1 2 3 4 Next →

View Pre-Algebra Tutors

Stewart
Certified Tutor

University of North Texas, Bachelor of Science, Physical Education Teaching and Coaching. University of North Texas, Bachelor...

View Pre-Algebra Tutors

Jonathan
Certified Tutor

Bushnell University, Bachelor of Science, Mathematics.

View Pre-Algebra Tutors

Steven
Certified Tutor

Drexel University, Bachelor of Science, Biology, General.

All Pre-Algebra Resources

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

Popular Subjects

Math Tutors in New York City,ISEE Tutors in Seattle,Chemistry Tutors in Philadelphia,Reading Tutors in Phoenix,Algebra Tutors in Washington DC,Chemistry Tutors in Boston,Chemistry Tutors in Miami,Algebra Tutors in Los Angeles,Spanish Tutors in Los Angeles,GRE Tutors in Atlanta

Popular Courses & Classes

SSAT Courses & Classes in Denver,SSAT Courses & Classes in New York City,LSAT Courses & Classes in Los Angeles,Spanish Courses & Classes in Phoenix,SAT Courses & Classes in Philadelphia,MCAT Courses & Classes in San Diego,GMAT Courses & Classes in Denver,GRE Courses & Classes in Chicago,ACT Courses & Classes in Washington DC,LSAT Courses & Classes in Chicago

Popular Test Prep

ISEE Test Prep in Atlanta,ACT Test Prep in Washington DC,GRE Test Prep in Los Angeles,MCAT Test Prep in San Diego,SAT Test Prep in Philadelphia,SSAT Test Prep in Denver,ISEE Test Prep in Denver,ACT Test Prep in Houston,MCAT Test Prep in Philadelphia,SSAT Test Prep in Atlanta

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)

*请描述版权工作的马y 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 : Adding and Subtracting Polynomials

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #11 :Adding And Subtracting Polynomials

Example Question #12 :Adding And Subtracting Polynomials

Example Question #13 :Adding And Subtracting Polynomials

Example Question #14 :Adding And Subtracting Polynomials

Example Question #15 :Adding And Subtracting Polynomials

Example Question #16 :Adding And Subtracting Polynomials

Example Question #17 :Adding And Subtracting Polynomials

Example Question #18 :Adding And Subtracting Polynomials

Example Question #19 :Adding And Subtracting Polynomials

Example Question #20 :Adding And Subtracting Polynomials

All Pre-Algebra Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Find the Best Tutors

Email address:
Your name:
Feedback: