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Chapter 5: Q. 5.91 (page 550)

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

Short Answer

Expert verified

Yes, x-5is a factor of f(x)=x3-125

Step by step solution

01

Step 1. Given Information

We want to use the Factor Theorem to determine if x-5is a factor off(x)=x3-125

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� 5 is a factor off(x)=x3鈭�125iff(5)=0

f(x)=x3鈭�125

To evaluate f (5) substitute x = 5.

localid="1646127714553" f(5)=53鈭�125

Simplify.

f(5)=125鈭�125

Subtract.

f(5)=0

Sincef(5)=0, x鈭�5is a factor off(x)=x3鈭�125.

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