/*! 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 23 Use long division to divide. $... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 23

Use long division to divide. $$\left(3 x+2 x^{3}-9-8 x^{2}\right) \div\left(x^{2}+1\right)$$

Short Answer

Expert verified
The quotient of the division is \(2x - 10\).

Step by step solution

01

Rewriting the Polynomials

First, rewrite the polynomials in descending order of their degrees and include terms with zero coefficients (for missing degrees in the polynomial). Now, the division looks like this: \(2x^3 - 8x^2 + 3x - 9 \div x^2 + 0x + 1\).
02

Dividing the First Terms

Divide the first term of the dividend \(2x^3\) by the first term of the divisor \(x^2\) to get \(2x\). This becomes the first term of the result. Write it above the line in the quotient.
03

Multiplying and Subtracting

Take the result from Step 2, \(2x\), multiply it with the divisor \(x^2 + 0x + 1\), and subtract this result from the dividend. This gives the new dividend as \(-8x^2 + 3x - 2x^2 -0x -2\), which simplifies to -10x^2 + 3x - 2.
04

Repeating the Process

Repeat Steps 2 and 3 with the new dividend. Divide \(-10x^2\) by \(x^2\) to get -10. This becomes the next term of the result. Multiply the divisor by -10, subtract it from the new dividend, and get as a new dividend \(3x + 10x -10\), which simplifies to 13x - 10.
05

Final Division

Repeat Steps 2 and 3 again. This time, divide 13x by \(x^2\). Since the degree of \(x^2\) is higher than that of 13x, this results in 0. So, the division process stops.
06

Writing the Final Result

The final result of the division is \(2x - 10\). Therefore, the original expression, \(2x^3 - 8x^2 + 3x - 9 \div x^2 + 1\), simplifies to \(2x - 10\).

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

(a) Find the interval(s) for \(b\) such that the equation has at least one real solution and (b) write a conjecture about the interval(s) based on the values of the coefficients. $$2 x^{2}+b x+5=0$$

Find all real zeros of the function. $$g(x)=3 x^{3}-2 x^{2}+15 x-10$$

Write the polynomial as the product of linear factors and list all the zeros of the function. $$f(x)=x^{2}+36$$

Think About It Let \(y=f(x)\) be a cubic polynomial with leading coefficient \(a=-1\) and \(f(2)=f(i)=0\) Write an equation for \(f\)

Write the polynomial as the product of linear factors and list all the zeros of the function. $$h(x)=x^{3}-3 x^{2}+4 x-2$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Probability and Statistics

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.