/*! 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 18 Divide using synthetic division.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 18

Divide using synthetic division. $$\left(x^{2}+x-2\right) \div(x-1)$$

Short Answer

Expert verified
The quotient of the polynomial division is \(x+2\).

Step by step solution

01

Identify the Coefficients and Setup Synthetic Division

Write out the coefficients of the polynomial \(x^{2}+x-2\) we are dividing, which are [1, 1, -2]. Write out the value of 'x' from the divisor, \(x-1\), which gives us 1. Set up the synthetic division where the coefficients of the polynomial are on the top row and the 'x' value is on the left outside the division symbol.
02

Perform the Synthetic Division

Start synthetic division by bringing down the leading coefficient (1) in the dividend to the bottom row. Multiply this number by the divisor (1), and write the result (1) under the next coefficient in the top row. Add the numbers in this column together and write the sum underneath (1+1=2). Repeat this process with this new number (2). Multiply it with the divisor (2*1=2), write the result under the next coefficient, and add the column to get 0.
03

Write the Result

The final row of numbers represents the coefficients of the quotient. In our case, [1, 2, 0] represents the function \(x+2\). Thus, \((x^{2}+x-2) \div (x-1)\) results in \(x+2\).

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 equation of a rational function \(f(x)=\frac{p(x)}{q(x)}\) having the indicated properties, in which the degrees of \(p\) and \(q\) are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties. \(f\) has no vertical. horizontal, or slant asymptotes, and no \(x\) -intercepts.

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 factor affect the demand for your product?

Which one of the following is true? a. If \(f(x)=-x^{3}+4 x,\) then the graph of \(f\) falls to the left and to the right. b. A mathematical model that is a polynomial of degree \(n\) whose leading term is \(a_{n} x^{n}, n\) odd and \(a_{n}<0,\) is ideally suited to describe nonnegative phenomena over unlimited periods of time. c. There is more than one third-degree polynomial function with the same three \(x\) -intercepts. d. The graph of a function with origin symmetry can rise to the left and to the right.

In Exercises \(1-10\), determine which functions are polynomial functions. For those that are, identify the degree. $$g(x)=7 x^{5}-\pi x^{3}+\frac{1}{5} x$$

In Exercises \(35-50\) a. Use the Leading Coefficient Test to determine the graphs end behavior. b. Find \(x\) -intercepts by setting \(f(x)=0\) and solving the resulting polynomial equation. State whether the graph crosses the \(x\)-axis, or touches the \(x\)-axis and turns around, at each intercept. c. Find the \(y\) -intercept by setting \(x\) equal to 0 and computing \(f(0)\) d. Determine whether the graph has \(y\) -axis symmetry, origin symmetry, or neither. e. If necessary, find a few additional points and graph the function. Use the fact that the maximum number of turning points of the graph is \(n-1\) to check whether it is drawn correctly. $$f(x)=\frac{1}{2}-\frac{1}{2} x^{4}$$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

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.