/*! 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 83 Factor by grouping. $$3 x^{3}-... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 83

Factor by grouping. $$3 x^{3}-2 x^{2}-6 x+4$$

Short Answer

Expert verified
The factored form of the given polynomial by grouping method is \((3x - 2)(x^2 - 2)\)

Step by step solution

01

Group the Polynomial

Firstly, the given polynomial \(3x^3 - 2x^2 - 6x + 4\) can be divided into two groups: \(3x^3 - 2x^2\) and \(-6x + 4\).
02

Factor out the greatest common factor from each group

We factor out the GCF of each group separately. The GCF of \(3x^3 - 2x^2\) is \(x^2\), so we factor it out from the first group, and the GCF of \(-6x + 4\) is \(-2\), so we factor this one out from the second group. This gives us \(x^2(3x - 2) - 2(3x - 2)\).
03

Factor by Grouping

Now we can see that \(3x - 2\) is a common factor in both terms, so we group them together as: \((3x - 2)(x^2 - 2)\).

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

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. $$21 x^{2}-25 x-4$$

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$b x^{2}-4 b+a x^{2}-4 a$$

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. $$100 y^{2}-49$$

Factor: \(9 x^{2}-16 .\)

Exercises 150鈥�152 will help you prepare for the material covered in the next section. Evaluate \((3 x-1)(x+2)\) for \(x=\frac{1}{3}\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

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.