Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Variables

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

For the equation $x^{2}-10x+21=0$ , what is(are) the solution(s) for ?

Possible Answers:

3,7

-3,-7

2,5

Correct answer:

3,7

Explanation:

$x^{2}-10x+21=0$ , can be factored to (x -7)(x-3) = 0. Therefore, x-7 = 0 and x-3 = 0. Solving for x in both cases, gives 7 and 3.

Report an Error

Example Question #51 : Variables

Simplify:

$\frac{x^2+3x+4x+12}{x+4}$

Possible Answers:

$\frac{x^2+7x+12}{x+4}$

x-4

x+4

x-3

x+3

Correct answer:

x+3

Explanation:

In order to begin this kind of a problem, it's key to look at parts of the rational expression that can be simplified.

In this case, the denominator is an already-simplified binomial; however, the numerator can be factored through "factoring by grouping." This can be a helpful idea to keep in mind when you come across a polynomial with four terms and simplifying is involved.

${x^2+3x+4x+12}$ can be simplified first by removing the common factor of from the first two terms and the common factor of from the last two terms:

x(x+3)+4(x+3)

This leaves two terms that are identical (x+3) and their coefficients, which can be combined into another term to complete the factoring:

(x+4)(x+3)

Consider the denominator; the quantity (x+4) appears, so the (x+4) in the numerator and in the denominator can be cancelled out. The simplified expression is then left as (x+3) .

Report an Error

Example Question #1 : Binomial Denominators

Simplify:

$\frac{x^2+9x-10}{x-1}$

Possible Answers:

(x-1)

(x+1)

(x-10)

(x+2)

(x+10)

Correct answer:

(x+10)

Explanation:

In order to begin this kind of a problem, it's key to look at parts of the rational expression that can be simplified.

In this case, the denominator is an already-simplified binomial; however, the numerator can be factored.

x^2+9x-10

The roots will be numbers that sum up to but have the product of .

The options include:

(-1)(10) = -10
(1)(-10) = -10
(2)(-5) = -10
(-2)(5)= -10

When these options are summed up:

-1+10=9
1-10=-9
2-5=-3
-2+5=3

We can negate the last three options because the first option of and fulfill the requirements. Therefore, the numerator can be factored into the following:

${x^2+9-10}=(x-1)(x+10)$

Because the quantity (x-1) appears in the denominator, this can be "canceled out." This leaves the final answer to be the quantity (x+10) .

Report an Error

Example Question #641 : Algebra

Solve for x when 6x – 4 = 2x + 5

Possible Answers:

9/4

1/4

Correct answer:

9/4

Explanation:

Solve by simplifying:

6x – 4 = 2x + 5

6x = 2x + 9

4x = 9

x = 9/4

Report an Error

Example Question #1 : How To Simplify Binomials

What is the value of the following equation if t = 3 and v = –4 ?

$\small 2t^2+4vt+2v^2$

Possible Answers:

Correct answer:

Explanation:

Substitute the numbers 3 and –4 for t and v, respectively.

$\small 2(3)^2+4(-4)(3)+2(-4)^2$

$\small 18+(-48)+32=2$

Report an Error

Example Question #3 : How To Simplify Binomials

Simplify the following binomial:

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

Possible Answers:

x^2 + 8x - 2

2x^2 - 4x +16

x^2 - 4x +4

x^2 + 4x - 4

x^2 + 8x -4

Correct answer:

x^2 + 8x - 2

Explanation:

The equation that is presented is:

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

To get the correct answer, you first need to combine all of the like terms. So, you can subtract the 2x^2 from the 4x^2 , leaving you with:

2x^2 + 16x - 4

From there, you can reduce the numbers by their greatest common denominator, in this case, :

x^2 + 8x - 2

Then you have arrived at your final answer.

Report an Error

Example Question #2 : How To Simplify Binomials

Simplify the following binomial expression:

16x^2 - 14x + 12x - 8 + 2

Possible Answers:

x^2 - 8x - 3

8x^2 + 2x -3

8x^2 - x - 3

4x^2 - 4x - 4

2x^2 - 4x - 3

Correct answer:

8x^2 - x - 3

Explanation:

First, combine all of the like terms that you are able:

16x^2 - 2x - 6

Then, reduce by the greatest common denominator (in this case, ):

8x^2 - x - 3

Report an Error

Example Question #2 : How To Simplify Binomials

Simplify the following binomial:

$17x^{2} - 15x + 3x^{2 }+10x$

Possible Answers:

5x^2(4x-x)

5x(4x-1)

5(4x-x)

10x^2 - x

5x^2 - 3x

Correct answer:

5x(4x-1)

Explanation:

The equation presented in the problem is:

$17x^{2} - 15x + 3x^{2 }+10x$

First you have to combine the like terms, i.e. combining all instances of x^2 and :

20x^2 - 5x

Then, you can factor out the common to get your answer

5x(4x-1)

Report an Error

Example Question #1 : Binomials And Foil

Which of the following expressions is equivalent to: 6x (m²+yx²–3)?

Possible Answers:

6xm² + 6yx² -18x

xm² + 7x³ -18

6xm² + 6yx³ -18

6xm² + 7x³ -18

6xm² + 6yx³ -18x

Correct answer:

6xm² + 6yx³ -18x

Explanation:

6x (m²+yx²–3)= 6x∙m²+ 6xyx² – 6x∙3= 6xm² + 6yx³-18x (Use Distributive Property)

Report an Error

Example Question #1 : How To Multiply Binomials With The Distributive Property

Which of the following expressions is equivalent to: $7x(x^{2}+xz^{2}-7)$ ?

Possible Answers:

$x^{3}+x^{2}z^{2}-49x$

$7x^{3}+7x^{2}z^{2}-49$

$7x^{3}+7x^{2}z^{2}-49x$

$7x^{2}+x^{2}z^{2}-49x$

$7x^{3}+7z^{2}-49x$

Correct answer:

$7x^{3}+7x^{2}z^{2}-49x$

Explanation:

Use the distributive property to multiply by all of the terms in $(x^{2}+xz^{2}-7)$ :

$(7x\cdot x^{2})+(7x\cdot xz^{2}) + (7x\cdot -7)=$

$7x^{3}+7x^{2}z^{2}-49x$

Report an Error

View ACT Math Tutors

Sharon
Certified Tutor

Tabor College, Bachelor of Science, Mathematics Teacher Education. Tabor College, Masters in Education, Education.

View ACT Math Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

View ACT Math Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

GRE Courses & Classes in Seattle, MCAT Courses & Classes in Miami, ISEE Courses & Classes in San Diego, ACT Courses & Classes in Atlanta, GMAT Courses & Classes in Philadelphia, MCAT Courses & Classes in Boston, SAT Courses & Classes in Seattle, SAT Courses & Classes in Phoenix, LSAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Phoenix

Popular Test Prep

MCAT Test Prep in Boston, SSAT Test Prep in Atlanta, SAT Test Prep in Los Angeles, ISEE Test Prep in Boston, GMAT Test Prep in Atlanta, LSAT Test Prep in Philadelphia, GMAT Test Prep in Washington DC, LSAT Test Prep in New York City, SSAT Test Prep in Los Angeles, SSAT Test Prep in Houston

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

ACT Math : Variables

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

Example Question #51 : Variables

Example Question #1 : Binomial Denominators

Example Question #641 : Algebra

Example Question #1 : How To Simplify Binomials

Example Question #3 : How To Simplify Binomials

Example Question #2 : How To Simplify Binomials

Example Question #2 : How To Simplify Binomials

Example Question #1 : Binomials And Foil

Example Question #1 : How To Multiply Binomials With The Distributive Property

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: