/*! 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 121 Factor completely. $$y^{7}+y$$... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 121

Factor completely. $$y^{7}+y$$

Short Answer

Expert verified
The complete factorization of \(y^{7}+y\) is \(y(y^{6}+1)\).

Step by step solution

01

- Identifying the Greatest Common Factor (GCF)

Here, the GCF is a common term that can be factored out from every term of the given polynomial. For the expression \(y^{7}+y\), the GCF is \(y\), because it is a factor of both \(y^{7}\) and \(y\).
02

- Factoring Out the GCF

Divide each term of the polynomial by the GCF and rewrite the polynomial as the product of the GCF and the resulting expression. So, \(y^{7}+y\) will be factored as \(y(y^{6}+1)\).
03

- Checking for Further Factorization

Now, check if the expression \(y^{6}+1\) can be factored further. The expression \(a^{2}+1\) can't be factored, but \(a^{2}+1 = (a+ i)(a- i)\) in complex numbers where 'i' is a imaginary unit with the property that \(i^{2} = -1\). So, \(y^{6}+1\) can be re-written as \((y^{2}+1)(y^{4}-y^{2}+1)\). But considering real numbers, \(y^{6}+1\) can't be factored further.

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

Factor completely. $$4 x^{4}-9 x^{2}+5$$

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

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. $$10 x^{4}+20 x^{3}+15 x^{2}$$

Factor completely. $$x^{2}+8 x+16-25 a^{2}$$

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. $$y^{3}+2 y^{2}-4 y-8$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.