/*! 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 45 Use synthetic division to divide... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 45

Use synthetic division to divide. \(\frac{4 x^{3}+16 x^{2}-23 x-15}{x+\frac{1}{2}}\)

Short Answer

Expert verified
The final polynomial after synthetic division is \(4x^2 + 14x -7 - 30/x+\frac{1}{2}\)

Step by step solution

01

Setting Up the Synthetic Division

First rearrange the divisor in the form \(x - a\). Since it is given as \(x + 1/2\), we will change signs and take \(a = -1/2\). Write down the coefficients of the polynomial which needs to be divided. They are \(4, 16, -23, -15\). Write the divisor \(-1/2\) to the left of a vertical bar and the coefficients to the right of the bar. Missing powers require a coefficient of 0. There are no missing powers in this polynomial.
02

Perform Synthetic Division

Start the division process by bringing down the leading coefficient (4) as is. This value now starts the first position of the quotient. Multiply this value by your divisor \((-1/2)\), and write the result (\(-2\)) beneath the next coefficient (16) and add them to get 14. This updated value represents the next coefficient in quotient. Repeat the process for the remaining coefficients. The last value obtained is the remainder.
03

Write Down the Answer

The final line of numbers represents the coefficients of the answer. Because we divided by a linear factor, the degree of the result will be one less than the degree of the original polynomial. Therefore, as a result, we have a quadratic polynomial. Formulate the polynomial using these coefficients. The remainder is the constant term in the resulting polynomial.

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 the inequality and graph the solution on the real number line. \((x+2)^{2} \leq 25\)

Find the domain of \(x\) in the expression. Use a graphing utility to verify your result. \(\sqrt{\frac{x}{x^{2}-9}}\)

The revenue and cost equations for a product are \(R=x(50-0.0002 x)\) and \(C=12 x+150,000\) where \(R\) and \(C\) are measured in dollars and \(x\) represents the number of units sold. How many units must be sold to obtain a profit of at least \(\$ 1,650,000 ?\) What is the price per unit?

Find the key numbers of the expression. \(\frac{x}{x+2}-\frac{2}{x-1}\)

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

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

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.