/*! 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 49 Factor each polynomial using the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 49

Factor each polynomial using the negative of the greatest common factor. $$-12 x^{2}+18$$

Short Answer

Expert verified
The factored polynomial using the negative of the greatest common factor is \(-6(2x^{2} - 3)\).

Step by step solution

01

Identify the Greatest Common Factor

The greatest common factor (GCF) of \(-12x^{2}\) and \(18\) is the largest factor that divides both. Here, the factors of -12 are \(卤1, 卤2, 卤3, 卤4, 卤6,\) and \( 卤12\), and the factors of 18 are \(卤1, 卤2, 卤3, 卤6, 卤9,\) and \(卤18\). The largest common factor that appears in both lists is 6.
02

Find the Negative of the GCF

The negative of the greatest common factor is simply \(鈭�6\).
03

Factor the Polynomial

The polynomial \(-12x^{2} + 18\) can be factored as \(-6(2x^{2} - 3)\). The common factor -6 is taken out and each term of \(-12x^{2}+18\) is divided by -6. This leaves \(2x^{2} - 3\) inside the brackets.

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. $$8 x^{5}-2 x^{3}$$

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. $$16 y^{2}+24 y+9$$

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. $$x^{4}+8 x$$

Contain polynomials in several variables. Factor each polynomial completely and check using multiplication. $$48 x^{4} y-3 x^{2} y$$

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. $$27 x^{2}+75$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

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.