Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Polynomials

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #916 : High School Math

Simplify the expression.

(2x^2)(5x^3)

Possible Answers:

10x

10x^5

7x^5

7x^6

10x^6

Correct answer:

10x^5

Explanation:

Since all terms are being multiplied, we can simplify by grouping like terms together.

(2x^2)(5x^3)

(2*5)(x^2*x^3)

To simplify the variable, we can add the exponents according to exponential identities.

$(2*5)(x^{2+3})$

10x^5

Report an Error

Example Question #2 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify the expression.

(3x^2y)(2xy^2)^2

Possible Answers:

12x^9y^9

36x^9y^9

36x^4y^5

12x^4y^5

Correct answer:

12x^4y^5

Explanation:

(3x^2y)(2xy^2)^2

Begin by distributing the exponent into the parentheses. Remember that each term in the parentheses must be squared.

(3x^2y)(4x^2y^4)

All terms are now being multiplied. To make it simpler, we can re-group by like terms.

(3*4)(x^2*x^2)(y*y^4)

Multiplying exponential terms with the same base allows us to add the exponents.

$12x^{2+2}y^{1+4}=12x^4y^5$

Report an Error

Example Question #21 : Polynomials

Which of the following is a simplified expression of X³X²?

Possible Answers:

$X^{6}$

$X\cdot X^{2}$

$X^{5}$

$X^{1}$

$X\cdot 6$

Correct answer:

$X^{5}$

Explanation:

When you multiply two exponential expressions with the same base, add the exponents to simplify the expression.

$X^{3}X^{2}=X^{5}$

Report an Error

Example Question #22 : Polynomials

Which of the following is an alternate expression of X³Y³?

Possible Answers:

$X^{6}$

$(XY)^{6}$

$(X\cdot Y)^{3}$

$(X\cdot Y)^{9}$

$(X+Y)^{3}$

Correct answer:

$(X\cdot Y)^{3}$

Explanation:

When you are required to multiply exponential expressions with different bases but the same exponent, you can simplify the expression by adding parentheses and only using the exponent one time.

$X^{3}Y^{3}=(X\cdot Y)^{3}$

Report an Error

Example Question #23 : Polynomials

Which of the following is equivalent to the expression:

$3^{6}\cdot3^{-4}$ ?

Possible Answers:

$\frac{1}{27}$

$\frac{1}{9}$

Correct answer:

Explanation:

Recall that when we are multiplying exponential expressions with the same base, we add the exponents and keep the base the same. Additionally, remember that adding a negative number is equivalent to subtracting.

$3^{6} \cdot3^{-4} = 3^{6 + -4} = 3^{2} = 9$

Report an Error

Example Question #24 : Polynomials

Simplify (x^3)(x^8)

Possible Answers:

$x^{24}$

$x^{14}$

$x^{13}$

$x^{11}$

Correct answer:

$x^{11}$

Explanation:

When multiplying the same variable raised to different powers, add the powers of each term together. In this case, add and together to find the power of the answer, .

Report an Error

Example Question #6 : How To Use The Product Rule For Exponents In Pre Algebra

Simplify the exponential expression.

$\small [(3x^2y^2)(4xy^3)]^0$

Possible Answers:

$\small 12x^3y^5$

undefined

Correct answer:

Explanation:

$\small [(3x^2y^2)(4xy^3)]^0$

Any number to the "zero" power is equal to .

(anything)^0=1

$\small [(3x^2y^2)(4xy^3)]^0=[12x^3y^5]^0=1$

Report an Error

Example Question #25 : Polynomials

Evaluate:

$x^{(2x-2)}*x^{(4-2x)}$

Possible Answers:

$x^{2}$

$x^{4x-6}$

$x^{2x}$

$x^{2x-4}$

$x^{4-x}$

Correct answer:

$x^{2}$

Explanation:

The product rule for exponents states that when like numbers are raised to a certain power, their exponents are added to one another.

$x^{m}*x^{n}=x^{(m+n)}$

$x^{2x-2}*x^{4-2x}=x^{(2x-2)+(4-2x)}$

Solve for the exponent equation.

(2x-2)+(4-2x)=2x-2+4+-2x

$\rightarrow 2$

Therefore,

$\dpi{100} x^{2x-2}*x^{4-2x}=x^{2}$ .

Report an Error

Example Question #1021 : High School Math

If A = 3x^2 + 26 x +108

and

B= 12x-13 ,

what is A-B ?

Possible Answers:

14x+95

$3x^{2}+14x+121$

3x^2+48x+131

14x+131

3x^2+14x+95

Correct answer:

$3x^{2}+14x+121$

Explanation:

To solve we must first write out what A-B is:

A-B=(3x^2+26x+108)-(12x-13)

Now,we can simplify. However, notice that when subtracting these terms, we subtract all terms in the parentheses. Remember when we subtract a negative number, it is the same as adding the number. This is illustrated in the simplification below.

(3x^2+26x+108)-(12x-13) = 3x^2+26x+108 - 12x- (-13)

This simplifies to 3x^2+26x+108 - 12x +13

Now we can combine like terms. Let's put those together and then simplify

3x^2+26x+108 - 12x +13=3x^2+(26x - 12x)+(108 +13) = 3x^2+14x+121

Report an Error

Example Question #1022 : High School Math

Simplify the expression below.

3x + 4 - (2x + 6)

Possible Answers:

5x - 2

x + 2

x + 10

x - 2

5x + 10

Correct answer:

x - 2

Explanation:

3x + 4 - (2x + 6)

When simplifying the addition or subtraction of polynomials, we want to combine like terms. First, when we have a negative sign outside our parentheses, we know that we need to distribute that negative; think of it as an imaginary and use the distributive property).

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

Then, we combine our like terms. Be careful when subtracting.

Rearrange the expression.

3x + 4 - 2x - 6 = 3x - 2x + 4 - 6

Combine terms and simplify.

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

Report an Error

View Tutors

Elizabeth
Certified Tutor

Clark Atlanta University, Bachelor of Science, Physics. Berry College, Doctor of Education, Curriculum and Instruction.

View Tutors

Tatiana
Certified Tutor

Moscow State Linguistic University, Bachelors, German. Moscow State Linguistic University, PHD, Germanic Languages .

View Tutors

Suley
Certified Tutor

American Public University System, Masters in Education, Curriculum and Instruction.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in New York City, Algebra Tutors in Houston, GRE Tutors in Philadelphia, MCAT Tutors in Los Angeles, GRE Tutors in Chicago, English Tutors in Washington DC, ACT Tutors in Seattle, Spanish Tutors in Atlanta, Math Tutors in Washington DC, Physics Tutors in New York City

Popular Courses & Classes

GMAT Courses & Classes in Denver, ACT Courses & Classes in New York City, GRE Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Denver, ISEE Courses & Classes in Seattle, LSAT Courses & Classes in Atlanta, ISEE Courses & Classes in Phoenix, SAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Philadelphia, Spanish Courses & Classes in Seattle

Popular Test Prep

ACT Test Prep in New York City, GRE Test Prep in San Diego, ISEE Test Prep in Boston, GMAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Washington DC, LSAT Test Prep in Chicago, ISEE Test Prep in Philadelphia, ACT Test Prep in Dallas Fort Worth, SSAT Test Prep in Houston, GMAT Test Prep in Denver

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

High School Math : Polynomials

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #916 : High School Math

Example Question #2 : How To Use The Product Rule For Exponents In Pre Algebra

Example Question #21 : Polynomials

Example Question #22 : Polynomials

Example Question #23 : Polynomials

Example Question #24 : Polynomials

Example Question #6 : How To Use The Product Rule For Exponents In Pre Algebra

Example Question #25 : Polynomials

Example Question #1021 : High School Math

Example Question #1022 : High School Math

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: