/*! 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 24 Divide using synthetic division.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 24

Divide using synthetic division. $$\left(x^{5}+4 x^{4}-3 x^{2}+2 x+3\right) \div(x-3)$$

Short Answer

Expert verified
\(x^{4} + 7x^{3} + 21x^{2} + 63x +189\)

Step by step solution

01

Arrange the coefficients and constants

Firstly, locate the coefficients of the polynomial \(x^{5}+4 x^{4}-3 x^{2}+2 x+3\). Any missing exponents should be filled in with a zero. The coefficients of the polynomial then become 1, 4, 0, -3, 2, and 3. Write these values out under a division bar. On the outside of the division bar, place the number of the divisor with its value changed (i.e., -3 becomes 3).
02

Begin the synthetic division process

The synthetic division process involves a series of operations: 'bring down, multiply, add, multiply, add' and so on. Let's begin: the first number (1) from the coefficients list is brought straight down, then is multiplied by the divisor's changed value (3). This result is placed in the next column and added to the corresponding original number (4), that gives 7. Continue these steps throughout the list.
03

Interpret the results

The final row of numbers are the coefficients of the answer. The number left over after all the coefficients are the remainder. In this case, there is no remainder. Hence, the numbers 1, 7, 21, 63, 189, and 570 create the polynomial \(x^{4} + 7x^{3} + 21x^{2} + 63x +189 + \frac{570}{x - 3}\). As there is no remainder, the final term can be discarded, leaving the resultant polynomial \(x^{4} + 7x^{3} + 21x^{2} + 63x +189\).

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

Begin by deciding on a product that interests the group because you are now in charge of advertising this product. Members were told that the demand for the product varies directly as the amount spent on advertising and inversely as the price of the product. However, as more money is spent on advertising, the price of your product rises. Under what conditions would members recommend an increased expense in advertising? Once you've determined what your product is, write formulas for the given conditions and experiment with hypothetical numbers. What other factors might you take into consideration in terms of your recommendation? How do these factors affect the demand for your product?

Whe lise a graphing utility to graph $$ f(x)=\frac{x^{2}-4 x+3}{x-2} \text { and } g(x)=\frac{x^{2}-5 x+6}{x-2} $$ What differences do you observe between the graph of \(f\) and the graph of \(g\) ? How do you account for these differences?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm working with a fourth-degree polynomial function with integer coefficients and zeros at 1 and \(3+\sqrt{5} .\) I'm certain that \(3+\sqrt{2}\) cannot also be a zero of this function.

The illumination from a light source varies inversely as the square of the distance from the light source. If you raise a lamp from 15 inches to 30 inches over your desk, what happens to the illumination?

What is a rational function?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Geometry

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.