/*! 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 34 Use synthetic division to divide... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 34

Use synthetic division to divide. \(\left(3 x^{3}-16 x^{2}-72\right) \div(x-6)\)

Short Answer

Expert verified
The result of the division \((3x^{3} - 16x^{2} - 72) \div (x-6)\) using synthetic division is \(3x^{2}+2x-12\).

Step by step solution

01

- Develop the Synthetic Division Setup

First, find the zero of the divisor \((x-6)\) which is \(6\). After that, write down the coefficients of the polynomial to be divided. So, write \(6\) and below write the coefficients of polynomial \((3, -16, 0, -72)\). Zero is written because the polynomial does not have the term with power \(x\), but it is necessary to consider every power of \(x\) from highest to lowest.
02

- Carry Out the Synthetic Division

Carry down the first coefficient which is \(3\). Multiply the divisor's zero (6) by the number just written below the line (-16), put the product below the next number (0), and add to get the new number below the line (which is -16). Repeat this process for each coefficient.
03

- Interpret the Result

After the synthetic division, the result obtained is the coefficients of the quotient. The last number (-12) is the remainder, read from bottom to top, a polynomial of one degree less than the original polynomial. Write the final result.

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

The graph of a rational function can never cross one of its asymptotes.

A driver averaged 50 miles per hour on the round trip between Akron, Ohio, and Columbus, Ohio, 100 miles away. The average speeds for going and returning were \(x\) and \(y\) miles per hour, respectively. (a) Show that \(y=\frac{25 x}{x-25}\). (b) Determine the vertical and horizontal asymptotes of the graph of the function. (c) Use a graphing utility to graph the function. (d) Complete the table. $$\begin{array}{|l|l|l|l|l|l|l|l|}\hline x & 30 & 35 & 40 & 45 & 50 & 55 & 60 \\\\\hline y & & & & & & & \\\\\hline\end{array}$$ (e) Are the results in the table what you expected? Explain. (f) Is it possible to average 20 miles per hour in one direction and still average 50 miles per hour on the round trip? Explain.

Find the domain of \(x\) in the expression. Use a graphing utility to verify your result. \(\sqrt{81-4 x^{2}}\)

(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. \(2 x^{2}+b x+5=0\)

Use a graphing utility to graph the rational function. Give the domain of the function and identify any asymptotes. Then zoom out sufficiently far so that the graph appears as a line. Identify the line. \(h(x)=\frac{12-2 x-x^{2}}{2(4+x)}\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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.