/*! 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 33 Use synthetic division to divide... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 33

Use synthetic division to divide. $$\left(-x^{3}+75 x-250\right) \div(x+10)$$

Short Answer

Expert verified
The result of the synthetic division is \(-x^{2}+10x-150 - \frac{1750}{x+10}\).

Step by step solution

01

Set Up Synthetic Division

Firstly, write the coefficients of the polynomial \(-x^3+75x-250\) in decreasing exponent order as \(-1, 0, 75, -250\). The zero is included for \(x^2\) because it is a missing term in the polynomial. Additionally, the divisor \(x+10\) is written as \(-10\) because synthetic division requires the root of the divisor, which is the value that makes the divisor 0.
02

Perform Synthetic Division

Start by bringing down the leading coefficient \(-1\) from the polynomial to the bottom row of the division. Multiply \(-10\) (the root) by \(-1\) (the number just brought down in the bottom row) which gives 10 and write this beneath the 0 in the top row. Add these two numbers (0 and 10) together to get 10 and write this in the bottom row. Repeat this process with the next numbers in the rows. Continue this process until all of the numbers in the top row have been calculated with.
03

Write the Answer

The numbers on the bottom row represents the coefficients of the quotient polynomial when the original polynomial is divided by the divisor, in decreasing order of exponent. So, for this example, starting from the left, -1 is the coefficient of \(x^{2}\), 10 is the coefficient of \(x^{1}\), and -150 is the constant term. The number -1750 represents the remainder of the division. This makes the final quotient \(-x^{2}+10x-150\), with a remainder of \(-1750\). Because the remainder is not 0, the quotient by itself is not the final answer. So the final answer will be \(-x^{2}+10x-150 - \frac{1750}{x+10}\).

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

Write the polynomial as the product of linear factors and list all the zeros of the function. $$f(x)=x^{3}-x^{2}+x+39$$

Write the polynomial as the product of linear factors and list all the zeros of the function. $$f(x)=5 x^{3}-9 x^{2}+28 x+6$$

Determine whether the statement is true or false. Justify your answer. The solution set of the inequality \(\frac{3}{2} x^{2}+3 x+6 \geq 0\) is the entire set of real numbers.

Use the information in the table to answer each question. $$\begin{array}{|c|c|} \hline \text { Interval } & \text { Value of } f(x) \\\\\hline(-\infty,-2) & \text { Positive } \\\\\hline(-2,1) & \text { Negative } \\\\\hline(1,4) & \text { Negative } \\\\\hline(4, \infty) & \text { Positive } \\\\\hline\end{array}$$ (a) What are the three real zeros of the polynomial function \(f ?\) (b) What can be said about the behavior of the graph of \(f\) at \(x=1 ?\) (c) What is the least possible degree of \(f ?\) Explain. Can the degree of \(f\) ever be odd? Explain. (d) Is the leading coefficient of \(f\) positive or negative? Explain. (e) Sketch a graph of a function that exhibits the behavior described in the table.

Find all real zeros of the function. $$f(z)=12 z^{3}-4 z^{2}-27 z+9$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete 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.