We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Understanding Quadratic Equations

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 #1 : Binomials

Expand:

(x-9)(3x+2)

Possible Answers:

$3x^{2}-29x-18$

$3x^{2}-18x-29$

$3x^{2}-25x-18$

$3x^{2}-18x-25$

None of the other answers

Correct answer:

$3x^{2}-25x-18$

Explanation:

To multiple these binomials, you can use the FOIL method to multiply each of the expressions individually.This will give you

(x)(3x)+(x)(2)+(-9)(3x)+(-9)(2)

or $3x^{2}-25x-18$ .

Report an Error

Example Question #11 : Trinomials

Evaluate the following:

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

Possible Answers:

2x^2+3x+8

2x^2-3x-8

x^2+3x-8

2x^2-3x

Correct answer:

2x^2-3x-8

Explanation:

To add these two trinomials, you will first begin by combining like terms. You have two terms with x^2 , two terms with , and two terms with no variable. For the two fractions with x^2 , you can immediately add because they have common denominators:

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

$\frac{4}{2}x^2 -3x - 8$

2x^2 -3x - 8

Report an Error

Example Question #12 : Understanding Quadratic Equations

Simplify.

$\small \small \frac{x^2+5x+6}{x^3+2x^2-16x-32}$

Possible Answers:

$\small \small \frac{x-3}{(x-4)(x+4)}$

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

$\small \small \frac{x-2}{(x-4)(x+4)}$

$\small \frac{x+3}{(x-4)(x+4)}$

$\small \small \frac{x+3}{(x+4)(x+4)}$

Correct answer:

$\small \frac{x+3}{(x-4)(x+4)}$

Explanation:

Factoring the expression gives $\small \frac{}{}$ $\small \small \frac{(x+3)(x+2)}{(x-4)(x+4)(x+2)}$ . Values that are in both the numerator and denominator can be cancelled. By cancelling $\small x+2$ , the expression becomes $\small \small \frac{(x+3)}{(x-4)(x+4)}$ .

Report an Error

Example Question #13 : Understanding Quadratic Equations

Simplfy.

$\small \frac{x^2-2x-15}{x^2-3x-10}$

Possible Answers:

$\small \small \frac{x-3}{x+2}$

$\small \frac{x+3}{x+2}$

$\small \small \small \frac{x-2}{x+3}$

$\small \small \frac{x+2}{x+3}$

$\small \small \frac{x+3}{x-2}$

Correct answer:

$\small \frac{x+3}{x+2}$

Explanation:

By factoring the equation you get $\small \small \small \frac{(x+3)(x-5)}{(x+2)(x-5)}$ . Values that are in both the numerator and denominator can be cancelled. Cancelling the $\small x-5$ values gives $\small \small \small \frac{x+3}{x+2}$ .

Report an Error

Example Question #14 : Understanding Quadratic Equations

Expand.

$\small 2(x+2)(x+4)$

Possible Answers:

$\small x^2+4x+8$

$\small \small 2x^2+12x-16$

$\small 2x^2+12x+16$

$\small \small x^2+4x-8$

$\small 2x+12x+16$

Correct answer:

$\small 2x^2+12x+16$

Explanation:

By foiling the binomials, multiplying the firsts, then the outers, followed by the inners and lastly the lasts, the expression you get is:

$\small 2(x^2+4x+2x+8)$ .

However, the expression can not be considered simplified in this state.

Distributing the two and adding like terms gives $\small 2x^2+12x+16$ .

Report an Error

Example Question #15 : Understanding Quadratic Equations

If (ax+b)(2ax+3b)=8x^2+30x+27 , what is the value of a-b ?

Possible Answers:

Correct answer:

Explanation:

Use the FOIL method to simplify the binomial.

(a+b)(c+d) = ac+ad+bc+bd

(ax)(2ax)+(ax)(3b)+(b)(2ax)+(b)(3b)

Simplify the terms.

2a^2x^2+5abx+3b^2=8x^2+30x+27

Notice that the coefficients can be aligned to the unknown variables. Solve for and .

$2a^2 = 8 \rightarrow a^2 = 4 \rightarrow a=2$

$3b^2 = 27\rightarrow b^2=9 \rightarrow b=3$

a-b = 2-3 = -1

The answer is:

Report an Error

Example Question #16 : Understanding Quadratic Equations

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

Possible Answers:

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

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

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

$\textup{The answer is not given.}$

3x^4-3x^3-x^2-2x-3

Correct answer:

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

Explanation:

Multiply each term of the first trinomial by second trinomial.

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

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

(-1)(3x^2-x+3) = -3x^2+x-3

Add and combine like-terms.

The answer is: 3x^4-4x^3+x^2-2x-3

Report an Error

Example Question #17 : Understanding Quadratic Equations

Simplify the function, if possible: $\frac{8x-10+2x^2}{-16+16x}$

Possible Answers:

$\frac{3}{16}x-\frac{3}{16}$

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

$\frac{1}{16}x-\frac{5}{16}$

$\textup{The expression cannot be factored.}$

$\frac{1}{16}x+\frac{5}{16}$

Correct answer:

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

Explanation:

The expression will need to be rearranged from highest to lowest powers in order to be simplified.

$\frac{8x-10+2x^2}{-16+16x} =\frac{2x^2+8x-10}{16x-16}$

Factor a 2 in the numerator.

2x^2+8x-10 = 2(x^2+4x-5)

Factor the term in parentheses.

2(x^2+4x-5) = 2(x-1)(x+5)

Factor the denominator.

16x-16 = 16(x-1)

Divide the numerator with the denominator.

$\frac{2(x-1)(x+5)}{16(x-1)}$

The expression becomes:

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

The answer is: $\frac{1}{8}x+\frac{5}{8}$

Report an Error

Example Question #18 : Understanding Quadratic Equations

Solve for x:

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

Possible Answers:

None of the other answers

-6,4

12,-2

-12,2

-4,6

Correct answer:

-6,4

Explanation:

The correct answer is x=-6 or x=4 . The first step of the problem is to cross multiply. This will give the following equation:

24=x^2+2x

After subtracting from each side the equation looks like:

0=x^2+2x-24

The expression on the right hand side can be factored into:

0=(x-4)(x+6 )

Both and satisfy the above equation and are therefore the correct answers.

Report an Error

Example Question #1 : Simplifying Polynomials

Expand this expression:

(x-4) (2x+4)

Possible Answers:

2x^2 + 4x + 16

2x^2 - 4x + 16

2x^2 - 4x - 16

2x^2 + 4x - 16

2x - 4x - 16

Correct answer:

2x^2 - 4x - 16

Explanation:

Use the FOIL method (First, Outer, Inner, Last):

x * 2x = 2x^2

x * 4 = 4x

-4 * 2x = -8x

-4 * 4 = -16

Put all of these terms together:

2x^2 + 4x - 8x - 16

Combine like terms:

2x^2 - 4x - 16

Report an Error

View Algebra 2 Tutors

Erica
Certified Tutor

University of Montevallo, Masters in Education, Mathematics Teacher Education.

View Algebra 2 Tutors

Reza
Certified Tutor

University of Sherbrooke, Doctor of Philosophy, Mathematics. University of Manitoba, Master of Science, Mathematics.

View Algebra 2 Tutors

Soung
Certified Tutor

University of Chicago, Bachelor in Arts, Chemistry. Northwestern University, Doctor of Science, Molecular Pharmacology.

All Algebra II Resources

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

Popular Subjects

Biology Tutors in New York City, Computer Science Tutors in New York City, English Tutors in Seattle, SSAT Tutors in Chicago, Reading Tutors in Boston, French Tutors in New York City, ACT Tutors in Los Angeles, LSAT Tutors in Chicago, SSAT Tutors in Dallas Fort Worth, Math Tutors in Los Angeles

Popular Courses & Classes

GRE Courses & Classes in Miami, MCAT Courses & Classes in Houston, ACT Courses & Classes in New York City, MCAT Courses & Classes in Phoenix, SSAT Courses & Classes in Washington DC, Spanish Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Phoenix, SSAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Los Angeles, ISEE Courses & Classes in Philadelphia

Popular Test Prep

ISEE Test Prep in Chicago, ACT Test Prep in Phoenix, ISEE Test Prep in Seattle, SAT Test Prep in Chicago, LSAT Test Prep in Miami, SSAT Test Prep in Seattle, MCAT Test Prep in Houston, ACT Test Prep in Dallas Fort Worth, GRE Test Prep in Los Angeles, GMAT Test Prep in Seattle

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 : Understanding Quadratic Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Binomials

Example Question #11 : Trinomials

Example Question #12 : Understanding Quadratic Equations

Example Question #13 : Understanding Quadratic Equations

Example Question #14 : Understanding Quadratic Equations

Example Question #15 : Understanding Quadratic Equations

Example Question #16 : Understanding Quadratic Equations

Example Question #17 : Understanding Quadratic Equations

Example Question #18 : Understanding Quadratic Equations

Example Question #1 : Simplifying Polynomials

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: