/*! 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. 5.92 Use the Factor Theorem to determ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Q. 5.92 (page 550)

Use the Factor Theorem to determine ifx鈭�6 is a factor of f(x)=x3鈭�216.

Short Answer

Expert verified

Yes,x-6is a factor off(x)=x3-216

Step by step solution

01

Step 1. Given Information

We want to use the Factor Theorem to determine if x-6is factor of f(x)=x3-216

We know that Factor Theorem:

For any polynomial function f (x),

鈥� if x 鈭� c is a factor of f (x), then f (c) = 0

鈥� if f (c) = 0, then x 鈭� c is a factor of f (x)

02

Step 2. Solve

The Factor Theorem tells us that x 鈭� 6 is a factor off(x)=x3-216iff(6)=0

f(x)=x3-216

To evaluate f (6) substitute x = 6.

f(6)=63-216

Simplify.

f(6)=216-216

Subtract.

f(6)=0

Sincelocalid="1646128264200" f(6)=0,x-6is a factor off(x)=x3-216

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

Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial. Then, find the degree of each polynomial (a)-5(b)8y3-7y2-y-3(c)-3x2y-5xy+9xy3(d)81m2-4n2(e)-3x6y3z

Subtractm2-7mn-3n2fromm2+n2

Convert (a) 1.6脳1010 (b) 8.43脳10-6 to decimal form.

Multiply (a) 2脳1021脳10-4 to get answer in decimal form

Divide (b)5脳10-21脳10-10to get answer in decimal form

Simplify4x332x54
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

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.