Chapter 5: Q. 5.92 (page 550)

Use the Factor Theorem to determine if $x - 6$ is a factor of $f (x) = x^{3} - 216$ .

Short Answer

Expert verified

Yes, $x - 6$ is a factor of $f (x) = x^{3} - 216$

Step by step solution

Step 1. Given Information

We want to use the Factor Theorem to determine if $x - 6$ is factor of $f (x) = x^{3} - 216$

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 − 6 is a factor of $f (x) = x^{3} - 216 i f f (6) = 0$

f (x) = x^{3} - 216

To evaluate f (6) substitute x = 6.

$f (6) = 6^{3} - 216$

Simplify.

$f (6) = 216 - 216$

Subtract.

$f (6) = 0$

Sincelocalid="1646128264200" $f (6) = 0, x - 6$ is a factor of $f (x) = x^{3} - 216$

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Use the Factor Theorem to determine if $x - 6$ is a factor of $f (x) = x^{3} - 216$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solve

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

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

Applied Mathematics

Logic and Functions

Discrete Mathematics

Statistics

Calculus

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Use the Factor Theorem to determine if $x - 6$ is a factor of $f (x) = x^{3} - 216$ .