/*! 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 25 Use synthetic division to divide... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 25

Use synthetic division to divide. $$\left(6 x^{3}+7 x^{2}-x+26\right) \div(x-3)$$

Short Answer

Expert verified
The quotient of the synthetic division is \(6x^{2} + 25x + 74\) and the remainder is 248.

Step by step solution

01

Setup Synthetic Division Tableau

First, make sure the polynomial is written in descending order of exponent. Then, write the coefficients (6, 7, -1, 26) in a row. The number to be put into the box is the opposite of the constant term in the divisor, which is \(x-3\) in this case. That constant becomes +3.
02

Carry Out Synthetic Division

Now carry out the synthetic division. Bring down the leading coefficient (6). Multiply 6 by 3 (value from the box), to get 18, and write this value underneath the second coefficient. Add 7 and 18 together to get 25, then multiply 25 by 3 to get 75. Write 75 under -1, giving 74. Multiply 74 by 3 to get 222 and add to 26 yielding 248.
03

Interpret the Result

The numbers on the bottom row of the tableau are the coefficients of the quotient polynomial. From left to right, these represent coefficients for \(x^{2}\), \(x^{1}\), \(x^{0}\), and the remainder, respectively. Hence, the result of the division is \(6x^{2} + 25x + 74\) with remainder 248

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

Use a graphing utility to graph the function and find its domain and range. $$f(x)=\sqrt{6+x^{2}}$$

Find all real zeros of the polynomial function. $$g(x)=8 x^{4}+28 x^{3}+9 x^{2}-9 x$$

Solve the inequality and sketch the solution on the real number line. Use a graphing utility to verify your solution graphically. \(3(x-5)<4 x-7\)

Use any convenient method to solve the quadratic equation. $$3 x^{2}-11 x-20=0$$

Simplify the expression. $$\left(\frac{x}{8}\right)^{-3}$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure 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.