/*! 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 39 Factor each polynomial using the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 39

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. $$10 x-20 x^{2}+5 x^{3}$$

Short Answer

Expert verified
The factored form of the given polynomial is \(5x(2 - 4x + x^{2})\).

Step by step solution

01

Identifying the greatest common factor

Check each term of the polynomial \(10x - 20x^{2} + 5x^{3}\). It's observed that the greatest common factor of all the terms is \(5x\).
02

Factoring out the greatest common factor

Pulling out the common factor, we get \(5x(2 - 4x + x^{2})\).
03

Check if the factored expression can be factored further

In the factored expression \(5x(2 - 4x + x^{2})\), the polynomial inside the parentheses cannot be factored further since there is no common factor in the terms and it does not meet any special factoring forms.

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. $$18 x^{3} y+57 x^{2} y^{2}+30 x y^{3}$$

Exercises 150鈥�152 will help you prepare for the material covered in the next section. Evaluate \(2 x^{2}+7 x-4\) for \(x=\frac{1}{2}\)

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. $$y^{5}-81 y$$

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

Factor completely. $$(y+1)^{3}+1$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Decision 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.