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Chapter 5: Q. 485 (page 563)

In the following exercises, use the Factor Theorem to determine if x-cis a factor of the polynomial function.

Determine whether x-2is a factor of x3-7x2+7x-6.

Short Answer

Expert verified

x-2is not a factor of x3-7x2+7x-6.

Step by step solution

01

Step 1. Given information.

The given expression is:

x3-7x2+7x-6

The other expression is x-2.

02

Step 2. Determine whether the expression is a factor or not.

According to the Factor Theorem, if f(c)=0then x-cis a factor of f(x).

The given expression can be written as:

f(x)=x3-7x2+7x-6

Evaluate f(2).

f(2)=(2)3-7(2)2+7(2)-6=8-28+14-6=-12

Since f(2)鈮�0, therefore x-2is not a factor of x3-7x2+7x-6.

03

Step 3. Conclusion.

x-2is not a factor of x3-7x2+7x-6.

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