/*! 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 26 Use synthetic division to divide... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 26

Use synthetic division to divide. $$\left(2 x^{3}+14 x^{2}-20 x+7\right) \div(x+6)$$

Short Answer

Expert verified
The result of the division \((2 x^{3}+14 x^{2}-20 x+7) \div(x+6)\) using synthetic division is \(2 x^{2} - 2 x - 8 - \frac{41}{x+6}\)

Step by step solution

01

Arrange the Coefficients for Synthetic Division

First, write down the coefficients of the dividend, which are the coefficients of the terms in order from highest to lowest degree. Here, the coefficients are \(2, 14, -20, 7\). Also, write down the number \(-6\), which is the opposite of the value of \(x\) from the divisor \(x + 6\).
02

Perform the Synthetic Division Operation

Bring down the leading coefficient (2 in this case) to the bottom row. Multiply this number by \(-6\) and write the product in the next column. Then add the numbers in this column and write the result on the bottom row. Repeat this procedure until all the columns are filled.
03

Interpret the Result

The last number in the bottom row is the remainder. The remaining numbers on the bottom row are the coefficients of the quotient. The degree of the terms in this quotient are one degree less than the degree of corresponding terms in the original dividend polynomial.
04

Write the Result

The result of the division can be written in the form quotient + remainder/divisor. In this case, the quotient is \(2 x^{2} - 2 x - 8\) and the remainder is \(-41\), thus the result can be expressed as \(2 x^{2} - 2 x - 8 - \frac{41}{x+6}\)

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

Divide using long division. $$\left(x^{2}+5 x+6\right) \div(x-4)$$

Find the value of \(k\) such that \(x-3\) is a factor of \(x^{3}-k x^{2}+2 k x-12\).

Write the general form of the equation of the line that passes through the points. $$(0,0),(-9,4)$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. \(|x+8|-1 \geq 15\)

Find the zeros (if any) of the rational function. Use a graphing utility to verify your answer. $$f(x)=\frac{x^{2}+4 x-21}{x^{2}-4 x+3}$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Decision 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.