/*! 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 38 Factor each trinomial, or state ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 38

Factor each trinomial, or state that the trinomial is prime. $$6 x^{2}-7 x y-5 y^{2}$$

Short Answer

Expert verified
The factorization of the trinomial \(6x^2-7xy-5y^2\) is \((3x-5y)(2x+y)\)

Step by step solution

01

Identify the structure of the trinomial

The given trinomial is \(6 x^{2}-7 x y-5 y^{2}\). This is a trinomial of the form \(ax^2+bxy + cy^2\).
02

Look for factors

Find two numbers that multiply to \(-30\) (\(a*c=-30\)) and add to \(-7\) (coefficient of the middle term). The numbers \(-10\) and \(3\) meet these criteria because \(-10*3=-30\) and \(-10+3=-7\).
03

Rewrite the trinomial

Rewrite the middle term \(-7xy\) of the trinomial as \(-10xy+3xy\). When you substitute this in the trinomial, you get: \(6x^2 - 10xy + 3xy - 5y^2\).
04

Group and factor terms

Observe for common factors in each binomial group - \(6x^2 - 10xy\) and \(3xy - 5y^2\). Factor out common terms: \(2x(3x-5y) + y(3x-5y)\).
05

Final factorization

Since both terms contain \((3x-5y)\), factor it out. This gives us the final factorization: \((3x-5y)(2x+y)\)

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

List all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. $$\left\\{-11,-\frac{5}{6}, 0,0.75, \sqrt{5}, \pi, \sqrt{64}\right\\}$$

Write each English phrase as an algebraic expression. Then simplify the expression. Let x represent the number. A number decreased by the sum of the number and four.

In Exercises \(83-90\), evaluate each expression without using a calculator. $$121^{\frac{1}{2}}$$

$$\text { factor completely.}$$ $$-x^{2}-4 x+5$$

Simplify the radical expressions in Exercises \(67-74\) if possible. $$\sqrt[3]{150}$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Mechanics 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.