We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Algebra II : Intermediate Single-Variable Algebra

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 #3 : Polynomials

Factor completely: $x^{2} - 9x - 20$

Possible Answers:

(x+10)(x-2)

(x-5)(x+4)

(x-10)(x+2)

The polynomial cannot be factored further.

(x+5)(x-4)

Correct answer:

The polynomial cannot be factored further.

Explanation:

We are looking to factor this quadratic trinomial into two factors (x+ ? )(x+?) , where the question marks are to be replaced by two integers whose product is and whose sum is .

We need to look at the factor pairs of in which the negative number has the greater absolute value, and see which one has sum :

$\begin{matrix} \textrm{Pair} & \textrm{Sum} \\ 1,-20& -19\\ 2,-10&-8 \\ 4,-5& -1 \end{matrix}$

None of these pairs have the desired sum, so the polynomial is prime.

Report an Error

Example Question #11 : Trinomials

Factor completely: $3y^{2} + y - 10$

Possible Answers:

$\left (y- 10 \right ) \left (3y +1\right )$

The polynomial cannot be factored further.

$\left (y- 2 \right ) \left (3y +5 \right )$

$\left (y+ 2 \right ) \left (3y -5 \right )$

$\left (y+ 10 \right ) \left (3y -1\right )$

Correct answer:

$\left (y+ 2 \right ) \left (3y -5 \right )$

Explanation:

Rewrite this as $3y^{2} + 1 y - 10$

Use the -method by splitting the middle term into two terms, finding two integers whose sum is 1 and whose product is 3 (-10) = -30 ; these integers are -5,6 , so rewrite this trinomial as follows:

$3y^{2} + 1 y - 10 = 3y^{2} -5y + 6 y - 10$

Now, use grouping to factor this:

$\left (3y^{2} -5y \right )+ \left (6 y - 10 \right )$

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

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

Report an Error

Example Question #3 : How To Factor An Equation

Factor the expression:

$\small 49r^2 - 36$

Possible Answers:

$\small (7r^2+6)(7r^2-6)$

$\small \small (7r+6)(7r-6)$

$\small prime$

$\small (7r^2-6)$

$\small (7r-6)^2$

Correct answer:

$\small \small (7r+6)(7r-6)$

Explanation:

The given expression is a special binomial, known as the "difference of squares". A difference of squares binomial has the given factorization: $\small a^2-b^2=(a+b)(a-b)$ . Thus, we can rewrite $\small 49r^2 - 36$ as $\small (7r)^2 - (6)^2$ and it follows that $\small (7r)^2-(6)^2=(7r+6)(7r-6).$

Report an Error

Example Question #4 : How To Factor An Equation

Factor the equation:

$x^{2}-6x+8$

Possible Answers:

(x-4)(x-2)

(x+4)(x+2)

(x-8)(x-2)

(x+4)(x-2)

(x-8)(x+2)

Correct answer:

(x-4)(x-2)

Explanation:

The product of (x+a)(x+b) is $x^{2}+ax+bx+ab$ .

For the equation $x^{2}-6x+8$ ,

a+b must equal and must equal .

Thus and must be and , making the answer (x-4)(x-2) .

Report an Error

Example Question #81 : Intermediate Single Variable Algebra

Find solutions to $x^{2}+x-6 = 0$ .

Possible Answers:

x=2,3

x=-3,2

x=-1,6

x=-6,1

x=-2,4

Correct answer:

x=-3,2

Explanation:

The quadratic can be solved as (x-2)(x+3)=0 . Setting each factor to zero yields the answers.

Report an Error

Example Question #41 : How To Factor A Polynomial

Factor:

x^2-25

Possible Answers:

(x+5)^2

The expression cannot be factored.

(x-5)^2

(x-5)(x+5)

x(x-25)

Correct answer:

(x-5)(x+5)

Explanation:

Because both terms are perfect squares, this is a difference of squares:

$\small x^2-25=x^2-5^2$

The difference of squares formula is a^2-b^2 = (a+b)(a-b) .

Here, a = x and b = 5. Therefore the answer is $\small (x-5)(x+5)$ .

You can double check the answer using the FOIL method:

$\small x^2-5x+5x-25= x^2-25$

Report an Error

Example Question #82 : Polynomials

Factor:

$\small x^2-5x+4$

Possible Answers:

$\small (x-1)(x-4)$

$\small (x+1)(x+4)$

$\small (x+1)(x-4)$

$\small (x-1)(x+4)$

Correct answer:

$\small (x-1)(x-4)$

Explanation:

The solutions indicate that the answer is:

$\small (x\ 1)(x\ 4)$ and we need to insert the correct addition or subtraction signs. Because the last term in the problem is positive (+4), both signs have to be plus signs or both signs have to be minus signs. Because the second term (-5x) is negative, we can conclude that both have to be minus signs leaving us with:

$\small (x-1)(x-4)$

Report an Error

Example Question #41 : Factoring Polynomials

Factor the following polynomial: x^2-2x-35 .

Possible Answers:

(x+5)(x-7)

(x+5)(x+7)

(x-1)(x+35)

(x-5)(x-7)

(x-35)(x-1)

Correct answer:

(x+5)(x-7)

Explanation:

Because the x^2 term doesn’t have a coefficient, you want to begin by looking at the term ( ax^2+bx+c ) of the polynomial: . Find the factors of that when added together equal the second coefficient (the term) of the polynomial.

There are only four factors of : 1, 5, 7, 35 , and only two of those factors, 5, 7 , can be manipulated to equal when added together and manipulated to equal when multiplied together: 5, -7 (i.e., 5-7=-2 ).

Report an Error

Example Question #11 : How To Factor A Variable

Factor the following polynomial: x^2+13x+30 .

Possible Answers:

(x-10)(x-3)

(x-5)(x-6)

(x+5)(x+6)

(x-10)(x+3)

(x+10)(x+3)

Correct answer:

(x+10)(x+3)

Explanation:

Because the x^2 term doesn’t have a coefficient, you want to begin by looking at the term ( ax^2+bx+c ) of the polynomial: .

Find the factors of that when added together equal the second coefficient (the term) of the polynomial: .

There are seven factors of : 1, 2, 3, 5, 6, 10, 15 , and only two of those factors, 3, 10 , can be manipulated to equal when added together and manipulated to equal when multiplied together: 3, 10

$3+10=13, 3\times10=30$

Report an Error

Example Question #1 : How To Find The Degree Of A Polynomial

Simplify:

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

Possible Answers:

None of the above

-1

Correct answer:

-1

Explanation:

The given expression can be re-written as:

$\frac{2x-5}{\left -(2x-5 \right )}$

Cancel (2x - 5):

$\frac{1}{-1} = -1$

Report an Error

View Algebra 2 Tutors

Michelle
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Mathematics.

View Algebra 2 Tutors

Dejuan
Certified Tutor

University of Illinois at Urbana-Champaign, Bachelor of Science, Electrical Engineering.

View Algebra 2 Tutors

Leonard
Certified Tutor

Florida State University, Bachelor of Science, Environmental Science.

All Algebra II Resources

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

Popular Subjects

Spanish Tutors in Los Angeles, Chemistry Tutors in Dallas Fort Worth, GMAT Tutors in Miami, English Tutors in Seattle, ISEE Tutors in Los Angeles, French Tutors in Washington DC, GRE Tutors in Dallas Fort Worth, SSAT Tutors in Chicago, Reading Tutors in San Diego, SAT Tutors in Washington DC

Popular Courses & Classes

ISEE Courses & Classes in Denver, GRE Courses & Classes in Miami, Spanish Courses & Classes in Houston, SAT Courses & Classes in Boston, SSAT Courses & Classes in Houston, ACT Courses & Classes in San Diego, ACT Courses & Classes in Washington DC, SSAT Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Chicago, ISEE Courses & Classes in San Francisco-Bay Area

Popular Test Prep

ISEE Test Prep in Chicago, SSAT Test Prep in Phoenix, MCAT Test Prep in Washington DC, GMAT Test Prep in Philadelphia, GMAT Test Prep in Miami, ISEE Test Prep in Boston, ACT Test Prep in Washington DC, GMAT Test Prep in Chicago, MCAT Test Prep in Houston, ACT Test Prep in San Diego

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 : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #3 : Polynomials

Example Question #11 : Trinomials

Example Question #3 : How To Factor An Equation

Example Question #4 : How To Factor An Equation

Example Question #81 : Intermediate Single Variable Algebra

Example Question #41 : How To Factor A Polynomial

Example Question #82 : Polynomials

Example Question #41 : Factoring Polynomials

Example Question #11 : How To Factor A Variable

Example Question #1 : How To Find The Degree Of A Polynomial

All Algebra II Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: