We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : How to subtract polynomials

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 #1 : How To Subtract Polynomials

Subtract the polynomials below:

(14a^2 + 2a - 5) - (10a^2 - 3a + 8)

Possible Answers:

4a^2 - a + 3

4a^2 + 5a - 13

24a^2 - a + 13

4a^2 + 5a + 3

4a^2 + 5a - 3

Correct answer:

4a^2 + 5a - 13

Explanation:

The first step is to get everything out of parentheses to combine like terms. Since the polynomials are being subtracted, the sign of everything in the second polynomial will be flipped. You can think of this as a being distributed across the polynomial:

(14a^2 + 2a - 5) - (10a^2 - 3a + 8)

=(14a^2 + 2a - 5) + -1(10a^2 - 3a + 8)

=14a^2 + 2a - 5 - 10a^2 + 3a - 8

Now combine like terms:

14a^2 + 2a - 5 - 10a^2 + 3a - 8

=4a^2 + 2a - 5 + 3a - 8

=4a^2 + 5a - 5 - 8

=4a^2 + 5a - 13

Report an Error

Example Question #1 : How To Subtract Polynomials

Simplify the expression: (5x^2z^4 + 4z^3y^3) - (2x^2z^4 - 3z^3y^3)

Possible Answers:

x^2 z^4+ y^3 z^3

Cannot be simplified further

3 x^2 z^4+7 y^3 z^3

3 x^4 z^8+7 y^6 z^6

Correct answer:

3 x^2 z^4+7 y^3 z^3

Explanation:

Don't be scared by complex terms! First, check to see if the variables are alike. If they match perfectly, we can add and subtract their coefficients just like we could if the expression was 3x - 3x .

Remember, a variable is always a variable, no matter how complex! In this problem, the terms match! So we just subtract the coefficients of the matching terms and we get our answer:

3 x^2 z^4+7 y^3 z^3

Report an Error

Example Question #1 : Simplifying Polynomials

Rewrite the expression in simplest terms.

$5x^{^{3}} - 14x^{2} - 10x + 3 - (4x+3) * x^{2} - (8-10x)$

Possible Answers:

5x^3 -17x^2 - 4x - 5

5x^3 -11x^2 - 24x - 5

x^3 - 11x^2 - 5

$x^{3}-17x^{2}-5$

x^3 - 11x^2 - 20x - 5

Correct answer:

$x^{3}-17x^{2}-5$

Explanation:

In simplifying this expression, be mindful of the order of operations (parenthical, division/multiplication, addition/subtraction).

$5x^{^{3}} - 14x^{2} - 10x + 3 - (4x+3) * x^{2} - (8-10x)$

Since operations invlovling parentheses occur first, distribute the factors into the parenthetical binomials. Note that the x^2 outside the first parenthetical binomial is treated as -x^2 since the parenthetical has a negative (minus) sign in front of it. Similarly, multiply the members of the expression in the second parenthetical by because of the negative (minus) sign in front of it. Distributing these factors results in the following polynomial.

5x^3 - 14x^2 - 10x + 3 - 4x^3 - 3x^2 - 8 + 10x

Now like terms can be added and subtracted. Arranging the members of the polynomial into groups of like terms can help with this. Be sure to retain any negative signs when rearranging the terms.

5x^3 - 4x^3 -14x^2 - 3x^2 - 10x + 10x + 3 - 8

Adding and subtracting these terms results in the simplified expression below.

x^3 - 17x^2 -5

Report an Error

Example Question #3 : Solving Rational Expressions

Solve:

$\frac{5}{x+1}-\frac{3x}{\left ( x+1 \right )\left ( x-2 \right )}= \frac{3}{x-2}$

Possible Answers:

$\frac{13}{2}$

Correct answer:

Explanation:

First we convert each of the denominators into an LCD which gives us the following:

$\frac{5\left ( x-2 \right )}{\left ( x+1 \right )\left ( x-2 \right )}- \frac{3x}{\left ( x+1 \right )\left ( x-2 \right )}= \frac{3\left ( x+1 \right )}{\left ( x+1 \right )\left ( x-2 \right )}$

Now we add or subtract the numerators which gives us:

$5\left ( x-2 \right )-3x= 3\left ( x+1 \right )$

Simplifying the above equation gives us the answer which is:

Report an Error

Example Question #1 : How To Subtract Polynomials

Simplify the following:

4x^3-2x(x-2)(x+3)

Possible Answers:

None of the other answers are correct.

4x^3-2x(x^2+x-6)

8x^3-2x+16

4x^3-2x^3-2x^2+12x

2x^3-2x^2+12x

Correct answer:

2x^3-2x^2+12x

Explanation:

4x^3-2x(x-2)(x+3)

First, FOIL the two binomials:

4x^3-2x(x^2+x-6)

Then distribute the through the terms in parentheses:

4x^3-2x^3-2x^2+12x

Combine like terms:

2x^3-2x^2+12x

Report an Error

Example Question #11 : Intermediate Single Variable Algebra

Simplify.

$(4a^{2}b+2ab) - (3a^{2}b+4ab+2)$

Possible Answers:

$a^{2}b+6ab+2$

$a^{2}b-2ab-2$

$a^{2}b+2ab-2$

$a^{2}b-6ab-2$

Correct answer:

$a^{2}b-2ab-2$

Explanation:

Simplify

$(4a^{2}b+2ab) - (3a^{2}b+4ab+2)$

Distribute the negative: $\boldsymbol{-}3a^{2}b\boldsymbol{-}4ab\boldsymbol{-}2$

Then combinde like terms

$\mathbf{\boldsymbol{-}3a^{2}b+4a^{2}b}(\mathbf{\boldsymbol{-}4ab+2ab})\boldsymbol{-}2$

Answer:

$a^{2}b-2ab-2$

Report an Error

Example Question #4 : How To Subtract Polynomials

Subtract:

$(7.5x^{2} + 1.4x - 4.6) - (x^{2} + 6.2x - 3.5)$

Possible Answers:

$6.5x^{2} - 4.8x - 1.1$

$7.5x^{2} - 4.8x - 1.1$

$7.5x^{2} +7.2x - 1.1$

$6.5x^{2} +7.2x - 1.1$

$6.5x^{2} - 4.8x - 8.1$

Correct answer:

$6.5x^{2} - 4.8x - 1.1$

Explanation:

$(7.5x^{2} + 1.4x - 4.6) - (x^{2} + 6.2x - 3.5)$

$= 7.5x^{2} + 1.4x - 4.6 - x^{2} - 6.2x + 3.5$

$= 7.5x^{2} - 1x^{2} + 1.4x- 6.2x - 4.6 + 3.5$

$= 6.5x^{2} - 4.8x - 1.1$

Report an Error

Example Question #82 : Expressions

Subtract:

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

Possible Answers:

$\frac{1}{4}x + \frac{5}{6}$

$-\frac{1}{4}x + \frac{5}{6}$

$\frac{1}{4}x + \frac{1}{9}$

$\frac{1}{4}x + \frac{1}{2}$

$-\frac{1}{4}x + \frac{1}{2}$

Correct answer:

$\frac{1}{4}x + \frac{5}{6}$

Explanation:

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

$=\frac{1}{2}x + \frac{2}{3} - \frac{1}{4}x + \frac{1}{6}$

$=\frac{1}{2}x - \frac{1}{4}x + \frac{2}{3} + \frac{1}{6}$

$=\frac{2}{4}x - \frac{1}{4}x + \frac{4}{6} + \frac{1}{6}$

$=\frac{1}{4}x + \frac{5}{6}$

Report an Error

Example Question #2 : How To Subtract Polynomials

Subtract:

$(7.5x^{2} + 2.4x - 4.6) - (x^{2} - 3.2x - 1.5)$

Possible Answers:

$6.5x^{2} + 5.6x - 3.1$

$6.5x^{2} -0.8x - 6.1$

$6.5x^{2} + 5.6x - 6.1$

$6.5x^{2} -0.8x - 3.1$

$7.5x^{2} + 5.6x - 3.1$

Correct answer:

$6.5x^{2} + 5.6x - 3.1$

Explanation:

$(7.5x^{2} + 2.4x - 4.6) - (x^{2} - 3.2x - 1.5)$

$= 7.5x^{2} + 2.4x - 4.6 - x^{2} + 3.2x +1.5$

$= 7.5x^{2} - 1x^{2} + 2.4x + 3.2x - 4.6 +1.5$

$= 6.5x^{2} + 5.6x - 3.1$

Report an Error

Example Question #1 : Elementary Operations

Subtract:

$\left (\frac{3}{4}x + \frac{2}{5} \right ) - \left (\frac{1}{8}x - \frac{1}{10} \right )$

Possible Answers:

$\frac{5}{8}x - \frac{1}{2}$

$\frac{5}{8}x + \frac{3}{10}$

$\frac{5}{8}x + \frac{1}{15}$

$\frac{5}{8}x - \frac{3}{10}$

$\frac{5}{8}x + \frac{1}{2}$

Correct answer:

$\frac{5}{8}x + \frac{1}{2}$

Explanation:

$\left (\frac{3}{4}x + \frac{2}{5} \right ) - \left (\frac{1}{8}x - \frac{1}{10} \right )$

$=\frac{3}{4}x + \frac{2}{5} - \frac{1}{8}x + \frac{1}{10}$

$=\frac{3}{4}x- \frac{1}{8}x + \frac{2}{5} + \frac{1}{10}$

$=\frac{6}{8}x- \frac{1}{8}x + \frac{4}{10} + \frac{1}{10}$

$=\frac{5}{8}x + \frac{5}{10}$

$=\frac{5}{8}x + \frac{1}{2}$

Report an Error

View Algebra Tutors

Stephanie
Certified Tutor

Cleveland State University, Bachelor of Science, Mathematics. University of Portland, Masters in Education, Curriculum and In...

View Algebra Tutors

William
Certified Tutor

University of Alabama at Birmingham, Bachelor of Science, Chemistry.

View Algebra Tutors

Armon
Certified Tutor

Loyola University-Chicago, Bachelor of Science, Biology, General. Columbia College-Chicago, Bachelor of Science, Graphic Desi...

All Algebra 1 Resources

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

Popular Subjects

Physics Tutors in Phoenix, GMAT Tutors in Houston, Calculus Tutors in Houston, Biology Tutors in Washington DC, MCAT Tutors in Denver, SSAT Tutors in Boston, ISEE Tutors in Washington DC, French Tutors in Los Angeles, Statistics Tutors in Miami, Calculus Tutors in New York City

Popular Courses & Classes

Spanish Courses & Classes in Atlanta, SSAT Courses & Classes in Philadelphia, LSAT Courses & Classes in New York City, ISEE Courses & Classes in Washington DC, Spanish Courses & Classes in Los Angeles, SSAT Courses & Classes in New York City, ISEE Courses & Classes in Atlanta, ACT Courses & Classes in Los Angeles, LSAT Courses & Classes in San Diego, GRE Courses & Classes in Dallas Fort Worth

Popular Test Prep

SAT Test Prep in New York City, ACT Test Prep in Seattle, GRE Test Prep in Philadelphia, SAT Test Prep in San Diego, ISEE Test Prep in Atlanta, LSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Washington DC, GRE Test Prep in Dallas Fort Worth, ISEE Test Prep in Chicago, LSAT Test Prep in Phoenix

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 : How to subtract polynomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Subtract Polynomials

Example Question #1 : How To Subtract Polynomials

Example Question #1 : Simplifying Polynomials

Example Question #3 : Solving Rational Expressions

Example Question #1 : How To Subtract Polynomials

Example Question #11 : Intermediate Single Variable Algebra

Example Question #4 : How To Subtract Polynomials

Example Question #82 : Expressions

Example Question #2 : How To Subtract Polynomials

Example Question #1 : Elementary Operations

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: