Q. 359 In the following examples, facto... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q. 359 (page 635)

In the following examples, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$x^{2} + 12 x y + 35 y^{2}$

Short Answer

Expert verified

The factors of the polynomial $x^{2} + 12 x y + 35 y^{2}$ is $(x + 5 y) (x + 7 y)$

Step by step solution

Step 1. Given

The trinomial is $x^{2} + 12 x y + 35 y^{2}$

To find the factors of the trinomial.

Step 2. Write binomial with first term x and second term y

The binomial contains $x$ in the the each term and $y$ in the second term.

The last and second term of the binomial is positive, so the factors must have positive signs.

$x^{2} + 12 x y + 35 y^{2} = (x +_y) (x +_y)$

Step 3. Find numbers multiply to 35 and add to 12

Find the numbers multiply to $35$ and add to $12$ .

Factors of $35$	Sum of factors
$1, 35$	$36$
$5, 7$	$12$

Step 4. Find the factors

Use $5, 7$ as coefficients of last term

$x^{2} + 12 x y + 35 y^{2} = (x + 5 y) (x + 7 y)$

Step 5. Check the answer

The factors are $(x + 5 y) (x + 7 y)$

Multiply the factors

$(x + 5 y) (x + 7 y) = x^{2} + 7 x y + 5 x y + 35 y^{2}$

$= x^{2} + 12 x y + 35 y^{2}$

Hence the multiplication of factors gives the trinomial.

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 examples, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$x^{2} + 12 x y + 35 y^{2}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Write binomial with first term x and second term y

Step 3. Find numbers multiply to 35 and add to 12

Step 4. Find the factors

Step 5. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Logic and Functions

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

91影视

In the following examples, factor each trinomial of the form x2+bxy+cy2x2+12xy+35y2

Short Answer

Step by step solution

Step 1. Given

Step 2. Write binomial with first term x and second term y

Step 3. Find numbers multiply to 35 and add to 12

Step 4. Find the factors

Step 5. Check the answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Theoretical and Mathematical Physics

Logic and Functions

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following examples, factor each trinomial of the form $x^{2} + b x y + c y^{2}$
$x^{2} + 12 x y + 35 y^{2}$