/*! 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 76 Find the quotient of \(x^{3 n}+1... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 76

Find the quotient of \(x^{3 n}+1\) and \(x^{n}+1\).

Short Answer

Expert verified
The quotient of \(x^{3 n} + 1\) divided by \(x^{n} + 1\) is \(x^{2n} - x^n + 1\).

Step by step solution

01

Identify Algebraic Identity

Identify the algebraic identity \(a^{3}+b^{3} = (a+b)(a^{2}-ab + b^{2})\). In this case, the cubic term \(x^{3 n} + 1\) can be rewritten as the sum of cubes, where \(a = x^n\) and \(b = 1\).
02

Applying the Identity

Apply the algebraic identity to \(x^{3 n} + 1\), this results in \((x^n + 1)(x^{2n} - x^n + 1)\).
03

Dividing By \(x^n+1\)

Now, in the given problem, we're to divide the expression by \(x^n + 1\). To do that, cancel off \(x^n + 1\) from both sides of the equation. The left over expression, \(x^{2n} - x^n + 1\), is the quotient of the division.

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

Solve each inequality using a graphing utility. $$ x^{3}+x^{2}-4 x-4>0 $$

A company is planning to manufacture mountain bikes The fixed monthly cost will be \(\$ 100,000\) and it will cost \(\$ 100\) to produce each bicycle. a. Write the cost function, \(C\), of producing \(x\) mountain bikes. b. Write the average cost function, \(\bar{C},\) of producing \(x\) mountain bikes c. Find and interpret \(\bar{C}(500), \bar{C}(1000), \bar{C}(2000),\) and \(\bar{C}(4000)\) \- d. What is the horizontal asymptote for the graph of the average cost function, \(\bar{C}\) ? Describe what this means in practical terms.

What does it mean if two quantities vary inversely?

Use everyday language to describe the behavior of a graph near its vertical asymptote if \(f(x) \rightarrow \infty\) as \(x \rightarrow-2\) and \(f(x) \rightarrow-\infty\) as \(x \rightarrow-2^{+}\)

Use inspection to describe each inequality's solution set. Do not solve any of the inequalities. $$(x-2)^{2} \leq 0$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.