/*! 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} Q. 20 Use the Remainder Theorem to fin... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q. 20 (page 209)

Use the Remainder Theorem to find the remainder when f(x)is divided by x-c. Then use the Factor Theorem to determine whether x-cis a factor of f(x).

f(x)=3x4+x3-3x+1;x+13

Short Answer

Expert verified

The remainder is2andx+13is not a factor.

Step by step solution

01

Step 1. Given information.

The given function is,

f(x)=3x4+x3-3x+1;x+13

02

Step 2. Using remainder theorem.

We know that if f(x)is divided by x-cthen the remainder will be f(c).

Here f(x)is divided by x+13, then the remainder is f-13that is

f-13=3-134+-133-3-13+1=127-127+1+1=2

Therefore, the remainder is 2.

03

Step 3. Using factor theorem.

We know that if x-cis the factor of the polynomial f(x)then

f(c)=0,

Here c=-13, then

f(c)=f-13=2

We observe that f-13鈮�0,then x+13is not a factor.

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

Graph each rational function using transformations.

R(x)=x2-4x2

United Parcel Service has contracted you to design a closed box with a square base that has a volume of 10,000cubic inches. See the illustration.

Part (a): Express the surface area S of the box as a function of x.

Part (b): Using a graphing utility, graph the function found in part (a).

Part (c): What is the minimum amount of cardboard that can be used to construct the box?

Part (d): What are the dimensions of the box that minimize the surface are?

Part (e): Why might UPS be interested in designing a box that minimizes the surface area?

In Problems 57鈥� 62, find the real zeros of f. If necessary, round to two decimal places.

f(x)=x3+3.2x2-7.25x-6.3

Can the graph of a polynomial function have no y-intercept? Can it have no x-intercepts? Explain.

Factor the expression6x2+x-2.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Applied 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.