/*! 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 13 Use long division to divide. $... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 13

Use long division to divide. $$\left(4 x^{3}-7 x^{2}-11 x+5\right) \div(4 x+5)$$

Short Answer

Expert verified
The result of the division is \(x^2 - 3x - \frac{3}{2}\)

Step by step solution

01

Setting up the Long Division

First, set up the polynomial division similar to how one would for numerical long division. Write \(4 x^{3}-7 x^{2}-11 x+5\) under the division symbol, and \(4 x + 5\) to the left of the division symbol
02

Dividing the First Term

Next, divide the first term of the dividend (\(4x^3\)) by the first term of the divisor (\(4x\)). This gives \(x^2\). Write that as the first term of the result quotient above the long division line.
03

Multiply and Subtract

Then, multiply the divisor by \(x^2\) and subtract this from \(4 x^{3}-7 x^{2}-11 x+5\). \((4x+5)x^2 = 4x^3+5x^2\). Subtracting gives \(-12x^2 - 11x + 5\)
04

Repeat the Process

Repeat this process for the new polynomial. Divide the first term, -12x^2, by 4x. This gives -3x, which you write as the next term of the quotient. Multiply the divisor by -3x and subtract, which gives -6x + 5.
05

Final Division and Result

Repeat one more time for -6x: Divide by 4x to get -\(\frac{3}{2}\), multiply the divisor and subtract to get a remainder of 0. The final result is \(x^2 - 3x - \frac{3}{2}\)

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

Match the cubic function with the numbers of rational and irrational zeros. (a) Rational zeros: \(0 ;\) irrational zeros: 1 (b) Rational zeros: \(3 ;\) irrational zeros: 0 (c) Rational zeros: \(1 ;\) irrational zeros: 2 (d) Rational zeros: \(1 ;\) irrational zeros: 0 $$f(x)=x^{3}-1$$

Decide whether the statement is true or false. Justify your answer. If \(x=-i\) is a zero of the function \(f(x)=x^{3}+i x^{2}+i x-1\) then \(x=i\) must also be a zero of \(f\)

Find all real zeros of the function. $$f(x)=4 x^{3}-3 x-1$$

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$f(x)=4 x^{3}-3 x^{2}+2 x-1$$

Write the polynomial as the product of linear factors and list all the zeros of the function. $$g(x)=2 x^{3}-x^{2}+8 x+21$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

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.