/*! 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 45 Factor each polynomial using the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 45

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. $$30 x^{2} y^{3}-10 x y^{2}+20 x y$$

Short Answer

Expert verified
The factored form of the polynomial \(30x^{2}y^{3}-10xy^{2}+20xy\) is \(10xy(3xy^2 - y + 2)\).

Step by step solution

01

Identify the GCF

Identify the greatest common factor (GCF) for all terms. Since we are dealing with both coefficients and variables, we need to find the GCF for both. The GCF of the coefficients 30, -10, and 20 is 10. The variables in each term are \(x^{2} y^{3}\), \(xy^{2}\), and \(xy\). The GCF in the variables' part is \(xy\) since it appears in all terms.
02

Divide each term by the GCF

Divide every term in the polynomial by the GCF. We will do this for both the coefficients and the variables: \[(30x^{2}y^{3} 梅 10xy)= 3xy^{2}\] \[(-10xy^{2} 梅 10xy) = -y\] \[(20xy 梅 10xy) = 2\]
03

Rewrite the polynomial

Rewrite the polynomial in factored form. Put the GCF out in front of the parentheses and write the results from step 2 inside the parentheses to obtain the factored form of the polynomial. The final answer should be \(10xy(3xy^2 - y + 2)\).

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

Exercises 150鈥�152 will help you prepare for the material covered in the next section. Factor: \((x-2)(x+3)-6\)

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

Factor completely. $$x^{2}+14 x+49-16 a^{2}$$

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 completely. $$5 y^{5}-5 y^{4}-20 y^{3}+20 y^{2}$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Applied 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.