Chapter 5: Q. 5.91 (page 550)

Use the Factor Theorem to determine if $x - 5$ is a factor of $f (x) = x^{3} - 125$ .

Short Answer

Expert verified

Yes, $x - 5$ is a factor of $f (x) = x^{3} - 125$

Step by step solution

Step 1. Given Information

We want to use the Factor Theorem to determine if $x - 5$ is a factor of $f (x) = x^{3} - 125$

We know that Factor Theorem

For any polynomial function f (x),

• if x − c is a factor of f (x), then f (c) = 0

• if f (c) = 0, then x − c is a factor of f (x)

Step 2. Solve

The Factor Theorem tells us that x − 5 is a factor of $f (x) = x^{3} - 125$ if $f (5) = 0$

f (x) = x^{3} - 125

To evaluate f (5) substitute x = 5.

localid="1646127714553" $f (5) = 5^{3} - 125$

Simplify.

$f (5) = 125 - 125$

Subtract.

$f (5) = 0$

Since $f (5) = 0$ , $x - 5$ is a factor of $f (x) = x^{3} - 125$ .

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Use the Factor Theorem to determine if $x - 5$ is a factor of $f (x) = x^{3} - 125$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use the Factor Theorem to determine if x−5 is a factor of f(x)=x3−125.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use the Factor Theorem to determine if $x - 5$ is a factor of $f (x) = x^{3} - 125$ .