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Chapter 6: Q 54E (page 573)

In the following exercises, factor.

x3+x2鈭�x鈭�1.

Short Answer

Expert verified

The factors for the expression x3+x2鈭�x鈭�1 are,x2-1x+1.

Step by step solution

01

Given expression is,

x3+x2鈭�x鈭�1.

The objective is, we need to find the factor for this expression.

02

First group each term with the common factors.

x3+x2鈭�x鈭�1=x3+x2+鈭�x鈭�1

Now factor out the common factors.

x3+x2鈭�x鈭�1=x2x+1-1x+1=x+1x2-1

The obtained factors are,x+1x2-1.

03

Step 3 let us check the answer by multiplying the factors.

x2-1x+1=x3+x2-x-1

which is true.

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