Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Polynomials

Study concepts, example questions & explanations for Algebra II

Create An Account

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Polynomials

Multiply the expressions:

$\small (x^{2} - 2x + 7) (x^{2} - 2x - 7)$

Possible Answers:

$\small x^{4}-4x^{3}+4x^2-49$

$\small \small x^{4}-4x^{3}+4x^2+49$

$\small \small \small x^{4}-4x^{3}-4x^2-49$

$\small \small \small \small \small x^{4}+4x^{3}-4x^2+49$

$\small \small \small \small x^{4}+4x^{3}-4x^2-49$

Correct answer:

$\small x^{4}-4x^{3}+4x^2-49$

Explanation:

You can look at this as the sum of two expressions multiplied by the difference of the same two expressions. Use the pattern

$\small (A+B)(A-B) = (A^{2}-B^{2})$ ,

where $\small A = x^{2} - 2x$ and $\small B = 7$ .

$\small \small \small (x^{2} - 2x + 7) (x^{2} - 2x - 7) = (x^{2} - 2x )^{2} - 7^{2} = (x^{2} - 2x )^{2} - 49$

To find $\small (x^{2} - 2x )^{2}$ , you use the formula for perfect squares:

$\small (A-B)^{2} = (A^{2}-2AB+B^{2})$ ,

where $\small \small A = x^{2}$ and $\small B = 2x$ .

$\small \small \small (x^{2}-2x)^{2} = ((x^{2})^{2}-2x^{2}(2x)+(2x)^{2}) = x^{4}-4x^{3}+4x^2$

Substituting above, the final answer is $\small x^{4}-4x^{3}+4x^2-49$ .

Report an Error

Example Question #1 : Polynomial Functions

Simplify:

$y=\frac{(x^2-16)(x+7)}{x+4}+(x-1)^2+13$

Possible Answers:

y=x^2-x-14

y=2(x^2+x-7)

$y=\frac{x^3+7x^2-16x-112}{x+4}+(x-1)^2+13$

$y=\frac{(x^2-16)(x+7)}{x+4}+x^2-2x+14$

y=2x^2+x-14

Correct answer:

y=2x^2+x-14

Explanation:

$y=\frac{(x^2-16)(x+7)}{x+4}+(x-1)^2+13$

First, factor the numerator of the quotient term by recognizing the difference of squares:

$y=\frac{(x-4)(x+4)(x+7)}{x+4}+(x-1)^2+13$

Cancel out the common term from the numerator and denominator:

y=(x-4)(x+7)+(x-1)^2+13

FOIL (First Outer Inner Last) the first two terms of the equation:

y=x^2+7x-4x-28+x^2-2x+1+13

Combine like terms:

y=2x^2+x-14

Report an Error

Example Question #11 : Simplifying Polynomials

$(3x^{2}-4xy+2y^{2})-(x^{2}+2xy-5y^{2})=?$

Possible Answers:

$4x^{2}-2xy+3y^{2}$

$2x^{2}-6xy-7y^{2}$

$2x^{2}-6xy+7y^{2}$

$4x^{2}-2xy-3y^{2}$

$2x^{2}+6xy-7y^{2}$

Correct answer:

$2x^{2}-6xy+7y^{2}$

Explanation:

$(3x^{2}-4xy+2y^{2})-(x^{2}+2xy-5y^{2})$

$=3x^{2}-4xy+2y^{2}-x^{2}-2xy+5y^{2}$

$=3x^{2}-x^{2}-4xy-2xy+2y^{2}+5y^{2}$

$=2x^{2}-6xy+7y^{2}$

Report an Error

Example Question #13 : Simplifying Polynomials

Expand:

$\tiny \tiny \tiny \tiny \small (2x-3y)(4x^{2}+6xy+9y^{2})$

Possible Answers:

$(2x-3y)^{2}$

$(2x-3y)(2x+3y)^{2}$

$8x^{3}-27y^{3}$

$(2x+3y)^{2}$

$8x^{3}+27x^{3}$

Correct answer:

$8x^{3}-27y^{3}$

Explanation:

$(2x-3y)(4x^{2}+6xy+9y^{2})$

$= 8x^{3}+12x^{2}y+18xy^{2}-12x^{2}y-18xy^{2}-27y^{2}$

$=8x^{3}-27y^{3}$

Report an Error

Example Question #13 : Simplifying Polynomials

Simplify

$\frac{2x^2-4x-30}{5-x}$

Possible Answers:

x+5

x+3

2x+6

-2x-6

2x+10

Correct answer:

-2x-6

Explanation:

The polynominal breaks down to 2(x-5)(x+3) , and once you factor out a from the denomintator and cancel, you are left with -2(x+3) .

Report an Error

Example Question #14 : Simplifying Polynomials

Simplify

$\frac{x^3+(x+2)^2+2x^2-x-3}{(x+1)^2}$

Possible Answers:

x^3+2x^2+x+2

$\frac{x^2+3x+3}{x-1}$

$\frac{x^3+3x^2+3x+1}{(x+1)^2}$

x+1

Correct answer:

x+1

Explanation:

First, you FOIL the binomial in the numerator. Then combine like terms, which simplifies the numerator to x^3+3x^2+3x+1 , which can be further simplified to (x+1)^3 . The coefficients for this can be found in Pascal's Triangle, so they do not have to be memorized. Once the numerator and denominator are in the same base, the exponents cancel out, leaving you with the correct answer.

Report an Error

Example Question #12 : Polynomials

Simplify the following expression

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

Possible Answers:

$6y^{2}+6x^{2}$

$7x^{2}-x+9y-3y^{2}$

Expresion cannot be simplified any further

$9y + 7x^{2} + 3xy^{2}$

$3y^{2}+x+9y+7x^{2}$

Correct answer:

$7x^{2}-x+9y-3y^{2}$

Explanation:

Simplify a polynomial expression by combining like terms. Like terms are those that have exactly the same variable and degree (exponent). This one is reasonably simple with only addition and subtraction of polynomials involved. The like terms are...

8y + y = 9y

$4x^{2}+3x^{2}=7x^{2}$

The remaining terms are $-3y^{2}$ and

Combine everything together as done below. As long as the signs are right, order of operations lets you arrange the final answer various ways, but you should know this be able to identify the correct answer even if yours was arranged differently.

$9y+7x^{2}-3y^{2}-x$

Report an Error

Example Question #91 : Polynomial Operations

Simplify

$(2x^{2}-5) + (4x^{3}-3x^{2}+2x-1)$

Possible Answers:

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

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

$4x^{3}-6x^{2}+1x-6$

$5x^{2}-6$

Correct answer:

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

Explanation:

$(2x^{2}-5) + (4x^{3}-3x^{2}+2x-1)$

To simplify you combind like terms:

$(4x^{3}\boldsymbol{-3x^{2}+2x^{2}} +2x\boldsymbol{-1-5)}$

Answer:

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

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

View Algebra 2 Tutors

Chelsea
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Physics. The University of Texas at Dallas, Master of Science, Bioinf...

View Algebra 2 Tutors

Ataul
Certified Tutor

Temple University, Bachelor of Science, Financial Planning.

View Algebra 2 Tutors

Mariam
Certified Tutor

Yarmouk University, Bachelor of Science, Mathematics. Touro College, Master of Science, Teacher Education, Multiple Levels.

All Algebra II Resources

10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Algebra Tutors in Phoenix, English Tutors in Washington DC, Math Tutors in Boston, GMAT Tutors in Atlanta, Calculus Tutors in New York City, LSAT Tutors in Miami, Biology Tutors in Boston, SSAT Tutors in Chicago, Computer Science Tutors in Houston, GMAT Tutors in Miami

Popular Courses & Classes

GRE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Washington DC, LSAT Courses & Classes in Houston, Spanish Courses & Classes in Miami, LSAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Denver, GRE Courses & Classes in Denver, MCAT Courses & Classes in Atlanta, MCAT Courses & Classes in Seattle

Popular Test Prep

ISEE Test Prep in Denver, SSAT Test Prep in San Francisco-Bay Area, GRE Test Prep in San Francisco-Bay Area, SAT Test Prep in Boston, SAT Test Prep in Philadelphia, SSAT Test Prep in Seattle, LSAT Test Prep in Denver, LSAT Test Prep in Houston, LSAT Test Prep in Chicago, SAT 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

Algebra II : Polynomials

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #11 : Polynomials

Example Question #1 : Polynomial Functions

Example Question #11 : Simplifying Polynomials

Example Question #13 : Simplifying Polynomials

Example Question #13 : Simplifying Polynomials

Example Question #14 : Simplifying Polynomials

Example Question #12 : Polynomials

Example Question #91 : Polynomial Operations

Example Question #11 : Intermediate Single Variable Algebra

Example Question #4 : How To Subtract Polynomials

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: