/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 33 Factor each polynomial using the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 33

Factor each polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. $$12 y^{2}+16 y-8$$

Short Answer

Expert verified
The polynomial \(12y^{2} + 16y - 8\) factored using the greatest common factor is \(4(3y^{2} + 4y - 2)\).

Step by step solution

01

Identify the Greatest Common Factor

Looking at the polynomial, \(12y^{2} + 16y - 8\), the coefficients are 12, 16 and -8. The greatest number that divides into these three numbers evenly is 4. So, the greatest common factor is 4.
02

Factor out the Greatest Common Factor

Divide each term in the original polynomial by the identified greatest common factor, 4. This gives the following: \(4(3y^{2} + 4y - 2)\).
03

Check the Result

Finally, check to ensure that the factored form cannot be factored further. After checking, it is observed that \(3y^{2} + 4y - 2\) has no common factors other than 1 so, it cannot be factored further. The factored form of the polynomial is thus \(4(3y^{2} + 4y - 2)\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$7 x^{5} y-7 x y^{5}$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$9 x^{4}+18 x^{3}+6 x^{2}$$

Factor completely. $$x^{2}+8 x+16-25 a^{2}$$

Factor completely. $$y^{7}+y$$

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$25 a^{2}+25 a b+6 b^{2}$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.