Q 123. In the following exercises, fact... [FREE SOLUTION]

91影视

Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 7: Q 123. (page 833)

In the following exercises, factor each expression. $m^{2} + m n - 56 n^{2}$

Short Answer

Expert verified

The factorization of $m^{2} + m n - 56 n^{2}$ is, $(m - 7 n) (m + 8 n)$ .

Step by step solution

Step 1. Given information

Given expression is $m^{2} + m n - 56 n^{2}$ .

Step 2. Find the last terms of the trinomials

Write the factors as trinomials, $m$ in the first term of each binomial and $n$ in the second term. $(m_n) (m_n)$

Find the numbers that multiply to $- 56$ and add to $1$ .

Factors of -56	Sum of factors
-1, 56	-1 + 56 = 55
-2, 28	-2 + 28 = 26
-4, 14	-4 + 14 = 10
-7, 8	-7 + 8 =1*
-56, 1	-56 + 1 = -55
-28, 2	-28 + 2 = -26
-14, 4	-14 + 4 = -10
-8, 7	-8 + 7 = -1

Step 3. Factorization

Use $- 7$ and $8$ as the last terms of the coefficents.

$m^{2} + m n - 56 n^{2} = (m - 7 n) (m + 8 n)$

Step 4. Check

$(m - 7 n) (m + 8 n) = m^{2} + 8 m n - 7 m n - 56 n^{2} = m^{2} + m n - 56 n^{2}$

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

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In the following exercises, factor each expression. $m^{2} + m n - 56 n^{2}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the trinomials

Step 3. Factorization

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Applied Mathematics

Logic and Functions

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

91影视

In the following exercises, factor each expression. m2+mn-56n2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the trinomials

Step 3. Factorization

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Applied Mathematics

Logic and Functions

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each expression. $m^{2} + m n - 56 n^{2}$