/*! 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 17 Use long division to divide. \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 17

Use long division to divide. \(\left(x^{3}-27\right) \div(x-3)\)

Short Answer

Expert verified
The result of the division \((x^{3} - 27) \div (x - 3)\) is \(x^{2} + 3x + 9\).

Step by step solution

01

Set up long division

Set it up the same way long division would be set up: divisor \((x - 3)\) on the left, dividend \((x^{3} - 27)\) on the right.
02

Divide the leading terms

Divide the first term of the dividend (\(x^{3}\)) by the first term of the divisor (\(x\)). Write the result (\(x^{2}\)) above the division bar.
03

Multiply and Subtract

Multiply the divisor \((x-3)\) by the result found in step 2 (\(x^{2}\)), write the result under the dividend and subtract it from the dividend. The result should be \(0x^{2} + 3x^{2} = 3x^{2}\).
04

Bring Down the Next Term

There are no more terms to bring down, so bring down the equivalent of zero or nothing. Then, divide the leading term of what's left in the dividend \(3x^{2}\) with the leading term in the divisor (\(x\)), giving a result of \(3x\). Write this above the bar.
05

Repeat steps 3 and 4

Multiply the divisor \((x-3)\) by the result found at step 4 (\(3x\)). Subtract this from what's left of the dividend. The end result is 0, which means that the division process is complete without any remainders.

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

Find a polynomial function that has the given zeros. 0,-7

A manufacturer wants to enlarge an existing manufacturing facility such that the total floor area is 1.5 times that of the current facility. The floor area of the current facility is rectangular and measures 250 feet by 160 feet. The manufacturer wants to increase each dimension by the same amount. (a) Write a function that represents the new floor \(\operatorname{area} A\). (b) Find the dimensions of the new floor. (c) Another alternative is to increase the current floor's length by an amount that is twice an increase in the floor's width. The total floor area is 1.5 times that of the current facility. Repeat parts (a) and (b) using these criteria.

Solve the inequality and graph the solution on the real number line. \(\frac{1}{x-3} \leq \frac{9}{4 x+3}\)

A company that manufactures bicycles estimates that the profit \(P\) (in dollars) for selling a particular model is given by \(P=-45 x^{3}+2500 x^{2}-275,000, \quad 0 \leq x \leq 50\) where \(x\) is the advertising expense (in tens of thousands of dollars). Using this model, find the smaller of two advertising amounts that will yield a profit of $$\$ 800,000\(.\)

The game commission introduces 100 deer into newly acquired state game lands. The population \(N\) of the herd is modeled by \(N=\frac{20(5+3 t)}{1+0.04 t}, \quad t \geq 0\) where \(t\) is the time in years (see figure). (a) Find the populations when \(t=5, t=10,\) and \(t=25 .\) (b) What is the limiting size of the herd as time increases?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

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.